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A posteriori error estimates and an adaptive finite element solution for the system of unsteady convection-diffusion-reaction equations in fluidized beds Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-20 V. Dhanya Varma; Suresh Kumar Nadupuri; Nagaiah Chamakuri
The a posteriori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived in this work. These are a system of five time dependent coupled nonlinear convection-diffusion-reaction equations. Based on the variational formulation, computable residual based a posteriori error estimates are obtained. The time discretization has been
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A fast and high-order numerical method for nonlinear fractional-order differential equations with non-singular kernel Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-20 Seyeon Lee; Junseo Lee; Hyunju Kim; Bongsoo Jang
Efficient and fast explicit methods are proposed to solve nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed methods produce the second-order for linear interpolation and the third-order accuracy for quadratic interpolation, respectively. The convergence analysis is proved by using discrete
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Two-dimensional Euler polynomials solutions of two-dimensional Volterra integral equations of fractional order Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-20 Yifei Wang; Jin Huang; Xiaoxia Wen
This paper proposes a method based on two-dimensional Euler polynomials combined with Gauss-Jacobi quadrature formula. The method is used to solve two-dimensional Volterra integral equations with fractional order weakly singular kernels. Firstly, we prove the existence and uniqueness of the original equation by Gronwall inequality and mathematical induction method. Secondly, we use two-dimensional
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Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-20 Zhong-Zhi Bai; Kang-Ya Lu
For a class of optimal control problems constrained with certain time- and space-fractional diffusive equations, by making use of mixed discretizations of temporal finite-difference and spatial finite-element schemes along with Lagrange multiplier approach, we obtain specially structured block two-by-two linear systems. We demonstrate positive definiteness of the coefficient matrices of these discrete
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Two-level defect-correction stabilized algorithms for the simulation of 2D/3D steady Navier-Stokes equations with damping Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-20 Bo Zheng; Yueqiang Shang
By combining the defect-correction method with the two-level discretization strategy and the local pressure projection stabilized method, this paper presents and studies two kinds of two-level defect-correction stabilized algorithms for the simulation of 2D/3D steady Navier-Stokes equations with damping, where the lowest equal-order P1−P1 finite elements are used for the velocity and pressure approximations
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A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-05 Jaemin Shin; Hyun Geun Lee
The epitaxial thin film growth model without slope selection is the L2-gradient flow of energy with a logarithmic potential in terms of the gradient of a height function. A challenge to numerically solving the model is how to treat the nonlinear term to preserve energy stability without compromising accuracy and efficiency. To resolve this problem, we present a high-order energy stable scheme by placing
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Computing the matrix sine and cosine simultaneously with a reduced number of products Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-19 Muaz Seydaoğlu; Philipp Bader; Sergio Blanes; Fernando Casas
A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be used in single and double precision arithmetic. The resulting algorithms are more efficient than schemes based on Padé approximations for a wide range of norm matrices
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Numerical Analysis of Linearly Implicit Euler-Riemann Method for Nonlinear Gurtin-MacCamy Model Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-19 Zhanwen Yang; Tianqing Zuo; Zhijie Chen
In this paper, we deal with the existence and stability of an equilibrium age distribution of the linearly implicit Euler-Riemann method for nonlinear age-structured population model with density dependence, i.e., the Gurtin-MacCamy models. It is shown that a dynamical invariance is replicated by numerical solutions for a long time. With the help of infinite-dimensional Leslie operators, the numerical
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A fractional spectral collocation method for general Caputo two-point boundary value problems Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-19 Haotao Cai; Qiguang An
In this paper we consider a fractional spectral collocation method for solving linear multi-term fractional differential equations involving Caputo-type fractional derivative. By using integral equation method, the boundary value problem of the fractional differential equation is reformulated as an equivalent Volterra-Fredholm integral equation with weakly singular kernels. Then we apply the fractional
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A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-11 Jinhong Jia; Hong Wang; Xiangcheng Zheng
We develop a preconditioned fast divided-and-conquer finite element approximation for the initial-boundary value problem of variable-order time-fractional diffusion equations. Due to the impact of the time-dependent variable order, the coefficient matrix of the resulting all-at-once system does not have a Toeplitz-like structure. In this paper we derive a fast approximation of the coefficient matrix
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Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-08 Zhengguang Liu; Shuangshuang Chen
In this paper, we propose a novel numerical approach to construct unconditionally energy stable schemes for the modified phase field crystal (MPFC) model. The new technique is based on the invariant energy quadratization (IEQ) method. The numerical schemes based on IEQ approach lead to time-dependent dense matrices, thus the fast Fourier transform (FFT) is difficult to be applied to solve the systems
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A circulant-matrix-based new accelerated GSOR preconditioned method for block two-by-two linear systems from image restoration problems Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-13 Min-Li Zeng
In this paper, we construct a circulant-matrix-based new accelerated GSOR (CNAGSOR) iteration method for a class of large and sparse block two-by-two linear systems of generalized saddle-point structure. Theoretical results about the convergence properties and eigenvalues distribution of the preconditioning matrix are studied in detail. Implementations in the image restoration problem and in the PDE-constraint
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The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-08 Mahboub Baccouch
In this paper, we propose an optimally convergent discontinuous Galerkin (DG) method for nonlinear third-order ordinary differential equations. Convergence properties for the solution and for the two auxiliary variables that approximate the first and second derivatives of the solution are established. More specifically, we prove that the method is L2-stable and provides the optimal (p+1)-th order of
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Interface adapted LBB-stable finite elements on fluid structure interaction problems in fully Eulerian framework Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-07 Harshin Kamal Asok
In this article, we implement and analyze a locally modified parametric finite element method for fluid structure interaction problems using LBB-stable finite elements. The variational formulation of the monolithically coupled fluid structure interaction problems is solved using a fully Eulerian framework. A combination of Q2-Q2-(Q1+Q0dc) and P2-P2-(P1+P0dc⁎) finite elements are used to approximate
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Fast spectral Petrov-Galerkin method for fractional elliptic equations Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-07 Zhaopeng Hao; Zhongqiang Zhang
In this work, we revisit the spectral Petrov-Galerkin method for fractional elliptic equations with the general fractional operators. To prove the optimal convergence of the method, we first present the ultra-weak formulation and establish its well-posedness. Then, based on such a novel formulation, we are able to prove the discrete counterpart and obtain the optimal convergence of the spectral method
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Spectral computation of low probability tails for the homogeneous Boltzmann equation Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-07 John Zweck; Yanping Chen; Matthew J. Goeckner; Yannan Shen
We apply the spectral-Lagrangian method of Gamba and Tharkabhushanam for solving the homogeneous Boltzmann equation to compute the low probability tails of the velocity distribution function, f, of a particle species. This method is based on a truncation, Qtr(f,f), of the Boltzmann collision operator, Q(f,f), whose Fourier transform is given by a weighted convolution. The truncated collision operator
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A high performance level-block approximate LU factorization preconditioner algorithm Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-06 Matthias Bollhöfer; Olaf Schenk; Fabio Verbosio
Many application problems that lead to solving linear systems make use of preconditioned Krylov subspace solvers to compute their solution. Among the most popular preconditioning approaches are incomplete factorization methods either as single-level approaches or within a multilevel framework. We will present a block incomplete factorization that is based on skillfully blocking the system initially
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Numerical investigations of shallow water waves via generalized equal width (GEW) equation Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-05 Seydi Battal Gazi Karakoc; Khaled Omrani; Derya Sucu
In this article, a mathematical model representing solution of the nonlinear generalized equal width (GEW) equation has been considered. Here we aim to investigate solutions of GEW equation using a numerical scheme by using sextic B-spline Subdomain finite element method. At first Galerkin finite element method is proposed and a priori bound has been established. Then a semi-discrete and a Crank-Nicolson
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Legendre spectral methods based on two families of novel second-order numerical formulas for the fractional activator-inhibitor system Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-06 Rumeng Zheng; Hui Zhang; Xiaoyun Jiang
In this paper, a novel numerical scheme is proposed to numerically solve the fractional activator-inhibitor system, which is a coupled nonlinear model. In the temporal direction, we employ two families of novel fractional θ-methods, the FBT-θ and FBN-θ methods, in spatial direction, the Legendre spectral method is used. Based on some positivity properties of the coefficients of both methods, the stability
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Linearized novel operational matrices-based scheme for classes of nonlinear time-space fractional unsteady problems in 2D Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-06 M. Usman; M. Hamid; R.U. Haq; M.B. Liu
Finding analytical and semi-analytical solutions of two-dimensional nonlinear fractional-order problems arising in mathematical physics is a challenging task for research community. In this work, an innovative scheme is proposed based on the shifted Gegenbauer wavelets. For this purpose first, we introduce shifted Gegenbauer polynomials via suitable transformation. Then, we present three-dimensional
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A least squares-based approach to evaluating strongly singular integrals Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-28 A. Castejón Lafuente; J.R. Illán González
The aim of this paper is to tackle the numerical calculation of the so-called finite-part integrals, including Cauchy principal value integrals and any supersingular integral. The numerical procedure consists of replacing the density function f(t) by the polynomial that is the best fit in a least-squares sense for the values f(zk), where {zk} is a set of distinct points located on an ellipse that surrounds
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Optimal superconvergence and asymptotically exact a posteriori error estimator for the local discontinuous Galerkin method for linear elliptic problems on Cartesian grids Appl. Numer. Math. (IF 1.979) Pub Date : 2021-01-04 Mahboub Baccouch
The purpose of this paper is twofold: to study the superconvergence properties and to present an efficient and reliable a posteriori error estimator for the local discontinuous Galerkin (LDG) method for linear second-order elliptic problems on Cartesian grids. We prove that the LDG solution is superconvergent towards a particular projection of the exact solution. The order of convergence is proved
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New primal-dual weak Galerkin finite element methods for convection-diffusion problems Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-23 Waixiang Cao; Chunmei Wang
This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard L2 norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.
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A fourth-order least-squares based reproducing kernel method for one-dimensional elliptic interface problems Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-17 Minqiang Xu; Lufang Zhang; Emran Tohidi
Increased attention has been paid on numerical modeling of interface problems as its wide applications in various aspects of science. Motivated by enhancing the application of the reproducing kernel, we focus on establishing a broken cubic spline spaces and developing a fourth-order numerical scheme for one-dimensional elliptic interface problems in this paper. The method is based on the least-squares
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On the recurrent computation of fractional operator with Mittag-Leffler kernel Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-22 Vsevolod Bohaienko
The paper considers the problem of computing the values of the Atangana-Baleanu derivative in Caputo sense which arises while solving fractional partial differential equations. In such case the values of the derivative are needed to be calculated in recurrent manner with increasing value of time or space variable. We consider series expansion and integral representations of the Mittag-Leffler function
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Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-16 Jiyong Li; Tingchun Wang
In this paper, we propose and analyze two conservative fourth-order compact finite difference schemes for the (1+1) dimensional nonlinear Dirac equation with periodic boundary conditions. Based on matrix knowledge, we convert the point-wise forms of the proposed compact schemes into equivalent vector forms and analyze their conservative and convergence properties. We prove that the proposed schemes
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A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-22 Yanjie Zhou; Yanan Zhang; Ye Liang; Zhendong Luo
This paper focuses on developing the reduced-order extrapolated model based on the splitting implicit finite difference (SIFD) scheme and the proper orthogonal decomposition (POD) for the two-dimensional (2D) fourth-order nonlinear Rosenau equation. For this purpose, we first construct the SIFD scheme and analyze the stability and convergence. And then, we develop a reduced-order extrapolated SIFD
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Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-15 Bhupen Deka; Naresh Kumar
In this paper, we consider the weak Galerkin finite element approximations of second order linear parabolic problems in two dimensional convex polygonal domains under the low regularities of the solutions. Optimal order error estimates in L2(L2) and L2(H1) norms are shown to hold for both the spatially discrete continuous time and the discrete time weak Galerkin finite element schemes, which allow
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Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-17 Jose Luis Gracia; Eugene O'Riordan
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The difference between this analytical function and the solution of the parabolic problem is approximated numerically. A coordinate transformation is used so that a
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Spectral approximation methods for non equilibrium transport in turbulent channel flows using fADE Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-16 Surath Ghosh; Snehasis Kundu; Sunil Kumar; Emad E. Mahmoud
In this work, the study of suspended sediment transport under unsteady, uniform and non equilibrium condition is extended using space fractional diffusion equation (fADE) with parameter α. Semi analytical solutions of this space fADE with realistic boundary conditions are obtained using spectral method developed on Chebyshev orthogonal polynomials. Solutions obtained from this method are compared with
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Higher order pathwise approximation for the stochastic Burgers' equation with additive noise Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-15 Feroz Khan
This article aims to investigate the pathwise convergence of the higher order scheme, introduced by Jentzen (2011) [9], for the stochastic Burgers' equation (SBE) driven by space-time white noise. In particular, first and second order derivatives of the non-linear drift term of the SBE are assumed to be defined and bounded in Sobolev spaces using the definition of distribution derivative i.e. Lemma
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Extended group finite element method Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-14 Kevin Tolle; Nicole Marheineke
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation interpolates nonlinear terms onto the finite element approximation space, we propose the use of a separate approximation space that is tailored to the nonlinearity. In many
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Local and parallel multigrid method for semilinear elliptic equations Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-15 Fei Xu; Qiumei Huang; Kun Jiang; Hongkun Ma
This paper presents a new type of local and parallel multigrid method to solve semilinear elliptic equations. The proposed method does not directly solve the semilinear elliptic equations on each layer of the multigrid mesh sequence, but transforms the semilinear elliptic equations into several linear elliptic equations on the multigrid mesh sequence and some low-dimensional semilinear elliptic equations
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An iterative scaling function procedure for solving scalar non-linear hyperbolic balance laws Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-15 Gino I. Montecinos
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose limiting function solves the original hyperbolic problem. Thus this gives rise to an iterative procedure. Its convergence is demonstrated both theoretically and analytically
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A meshless finite difference method for elliptic interface problems based on pivoted QR decomposition Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-09 Oleg Davydov; Mansour Safarpoor
We propose to solve elliptic interface problems by a meshless finite difference method, where the second order elliptic operator and jump conditions are discretized with the help of the QR decomposition of an appropriately rescaled multivariate Vandermonde matrix with partial pivoting. A prescribed consistency order is achieved on irregular nodes with small influence sets, which allows to place the
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A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-09 Shipeng Xu
In this paper, a posteriori error estimates for the Weak Galerkin finite element methods (WG-FEMs) for second order elliptic problems are derived in terms of an H1−equivalent energy norm. Corresponding estimators based on the helmholtz decomposition yield globally upper and locally lower bounds for the approximation errors of the WG-FEMs. Especially, the error analysis of our methods is proved to be
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A fast numerical method for fractional partial integro-differential equations with spatial-time delays Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-08 Ersin Aslan; Ömür Kıvanç Kürkçü; Mehmet Sezer
This study aims to efficiently solve the space-time fractional partial integro-differential equations with spatial-time delays, employing a fast numerical methodology dependent upon the matching polynomial of complete graph and matrix-collocation procedure. This methodology provides a sustainable approach for each computation limit since it arises from the durable graph structure of complete graph
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Preconditioners for multilevel Toeplitz linear systems from steady-state and evolutionary advection-diffusion equations Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-08 Xue-lei Lin; Micheal K. Ng; Andy Wathen
In this paper, we study preconditioners for multilevel Toeplitz linear systems arising from discretization of steady-state and evolutionary advection-diffusion equations, in which upwind scheme and central difference scheme are employed to discretize first-order and second-order terms, respectively. For the steady-state case, the preconditioner is constructed by replacing each of the discrete advection
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Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-02 M.H. Heydari; Z. Avazzadeh; A. Atangana
In this paper, we generalize a coupled system of nonlinear reaction-advection-diffusion equations to a variable-order fractional one by using the Caputo-Fabrizio fractional derivative, which is a non-singular fractional derivative operator. In order to establish an appropriate method for this system, we introduce a new formulation of the discrete Legendre polynomials namely the orthonormal shifted
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Generalized split feasibility problem for multi-valued Bregman quasi-nonexpansive mappings in Banach spaces Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-07 Suliman Al-Homidan; Bashir Ali; Yusuf I. Suleiman
In this paper, the notion of generalized split feasibility problem (GSFP) is studied in p-uniformly convex Banach spaces. Some special cases of the GSFP are highlighted. A self-adaptive step-size iterative algorithm which converges strongly to solution of the GSFP is proved. The implementation of the method is demonstrated with two numerical examples. Our method does not require prior information of
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High-order compact schemes for semilinear parabolic moving boundary problems Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-03 Tingyue Li; Dinghua Xu; Qifeng Zhang
In this paper, we study high-order compact schemes for semilinear parabolic moving boundary problems. We first convert the original problem into an equivalent one defined on a rectangular region by introducing a linear transformation and the well-known exponential transformation. Next, we derive a compact scheme with fourth-order accuracy in the spatial dimension and second-order accuracy in the temporal
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A new second-order modified hydrostatic reconstruction for the shallow water flows with a discontinuous topography Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-02 Jian Dong; Ding Fang Li
We consider a new second-order hydrostatic reconstruction (HR) based on the bottom topography, the depth-averaged velocity, and the water surface level for the shallow water flows with discontinuous bottom topography. The Audusse's second-order hydrostatic reconstruction (HR) (Audusse et al. (2004) [1]) fails to correctly reflect the wave pattern for the large discontinuous bottom topography. We propose
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A new finite difference scheme for the 3D Helmholtz equation with a preconditioned iterative solver Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-02 Tingting Wu; Yuran Sun; Dongsheng Cheng
In this paper, we propose a new finite difference scheme for the 3D Helmholtz problem, which is compact and fourth-order in accuracy. Different from a standard compact fourth-order one, the new scheme is specially established based on minimizing the numerical dispersion, by approximating the zeroth-order term of the equation with a weighted-average for the values at 27 points. To determine optimal
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Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-02 Hong Zhang; Jingye Yan; Xu Qian; Songhe Song
Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn equation has been an open problem in recent years. This work provides a positive answer by designing and analyzing a class of up to fourth order maximum principle preserving integrators for the Allen-Cahn equation. First, the second order finite difference discretization is applied to the Allen-Cahn equation in
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Numerical technique for fractional variable-order differential equation of fourth-order with delay Appl. Numer. Math. (IF 1.979) Pub Date : 2020-12-02 Sarita Nandal; Dwijendra Narain Pandey
In this paper, we construct a new efficient numerical scheme for variable fractional order differential equation of fourth order with delay. Here, we propose to use parametric quintic spline in the spatial dimension and L2−1σ formula for time dimension. The stability, convergence, and solvability are rigorously proved using discrete energy method. Our proposed scheme improves convergence in both aspects
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Convergence and numerical simulations of prey-predator interactions via a meshless method Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-26 J.J. Benito; A. García; L. Gavete; M. Negreanu; F. Ureña; A.M. Vargas
We study two mathematical models consisting of nonlinear systems of partial differential equations, a predator prey and a competitive two-species chemotaxis systems with two chemicals satisfying their corresponding elliptic equations in a smooth bounded domain. By introducing global factors, for different ranges of parameters and by deriving a discretization of the system by means of the Generalized
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On the ill-posed analytic continuation problem: An order optimal regularization scheme Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-26 Milad Karimi; Fridoun Moradlou; Mojtaba Hajipour
The main focus of this paper is on studying an order optimal regularization scheme based on the Meyer wavelets method to solve the analytic continuation problem in the high-dimensional complex domain Ω:={x+iy∈CN:x∈RN,‖y‖≤‖y0‖,y,y0∈R+N}. This problem is exponentially ill-posed and suffers from the Hadamard's instability. Theoretically, we first provide an optimal conditional stability estimate for the
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Linearly implicit GARK schemes Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-20 Adrian Sandu; Michael Günther; Steven Roberts
Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness and characteristic time scales. The multimethod approach discretizes each physical process with an appropriate numerical method; the methods are coupled appropriately such that the
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Moving least squares and spectral collocation method to approximate the solution of stochastic Volterra–Fredholm integral equations Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-20 Farshid Mirzaee; Erfan Solhi; Nasrin Samadyar
In this article, an idea based on moving least squares (MLS) and spectral collocation method is used to estimate the solution of nonlinear stochastic Volterra–Fredholm integral equations (NSVFIEs). The main advantage of the suggested approach is that in some parts where interpolation and integration are necessary, this approach does not require any meshes. Therefore, it is independent of the geometry
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Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-10 Nikhil Srivastava; Aman Singh; Yashveer Kumar; Vineet Kumar Singh
In this paper, we construct two efficient numerical schemes by combining the finite difference method and operational matrix method (OMM) to solve Riesz-space fractional diffusion equation (RFDE) and Riesz-space fractional advection-dispersion equation (RFADE) with initial and Dirichlet boundary conditions. We applied matrix transform method (MTM) for discretization of Riesz-space fractional derivative
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A new representation of generalized averaged Gauss quadrature rules Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-21 Lothar Reichel; Miodrag M. Spalević
Gauss quadrature rules associated with a nonnegative measure with support on (part of) the real axis find many applications in Scientific Computing. It is important to be able to estimate the quadrature error when replacing an integral by an ℓ-node Gauss quadrature rule in order to choose a suitable number of nodes. A classical approach to estimate this error is to evaluate the associated (2ℓ+1)-node
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A Modulus-Based Multigrid Method for Image Retinex Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-20 Li Sun; Yu-Mei Huang
Retinex theory shows that the color of a scene perceived by human visual system is only dependent on the intrinsic reflectance and unrelated to the illumination. For images recorded by digital cameras, the intensities are the product of the scene reflectance and illumination. Image intensities are different when taken under different illuminations. The aim of image retinex problem is to decompose the
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A singular value homotopy for finding critical parameter values Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-16 J.B. Collins; Jonathan D. Hauenstein
Various applications in science and engineering depend upon computing real solutions to systems of analytic equations which depend upon real parameters. Locally in the parameter space, the qualitative behavior of the solutions remains the same except at critical parameter values. This article develops a singular value homotopy that aims to compute critical parameter values. Several examples are presented
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IRK-WSGD methods for space fractional diffusion equations Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-18 Fu-Rong Lin; Yi-Feng Qiu; Zi-Hang She
In this paper, we develop high order numerical schemes for the solution of the initial-boundary value problem of one-dimensional and two-dimensional space fractional diffusion equations of orders belonging to the interval (1,2). Firstly, certain weighted and shifted Grünwald difference (WSGD) operator is used to approximate space Riemann-Liouville fractional derivatives, resulting in a linear system
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Partitioned exponential methods for coupled multiphysics systems Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-06 Mahesh Narayanamurthi; Adrian Sandu
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a
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A Riemannian nonmonotone spectral method for self-adjoint tangent vector field Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-12 Teng-Teng Yao; Fang Lu; Wei Li
Based on the requirement of specific problems, for instance unconstrained and equality-constrained Rayleigh quotient problems, we consider the problem of finding zeros of a tangent vector field on Riemannian manifold. More precisely, we focus on the study of self-adjoint tangent vector field in this paper. By making full use of the self-adjointness property of the tangent vector field, we propose an
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An hp-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-12 Lina Wang; Hongjiong Tian; Lijun Yi
We develop and analyze an hp-version of the discontinuous Galerkin time-stepping method for linear Volterra integral equations with weakly singular kernels. We derive a priori error bound in the L2-norm that is fully explicit in the local time steps, the local approximation orders, and the local regularity of the exact solutions. For solutions with singular behavior near t=0 caused by the weakly singular
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Quasi-uniform convergence analysis of rectangular Morley element for the singularly perturbed Bi-wave equation Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-10 Dongyang Shi; Yanmi Wu
A non-C0 rectangular Morley element method is discussed to solve the singularly perturbed Bi-wave equation and the penalty terms are included to guarantee convergence. The quasi-uniform convergence rate of order O(h) is derived in the energy norm irrelevant to the negative powers of the real perturbation parameter δ appearing in the considered problem, which improves an existing result, here h is the
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A modified SSOR-like preconditioner for non-Hermitian positive definite matrices Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-13 Sheng-Zhong Song; Zheng-Da Huang
A modified SSOR-like (MSSOR-like) preconditioner is constructed for a non-Hermitian positive definite linear system with a dominant Hermitian part. The eigenvalue distribution of the MSSOR-like preconditioned matrix and the convergence property of the corresponding MSSOR-like iteration method are discussed in depth. Numerical experiments show that the MSSOR-like preconditioner can lead to a high-speed
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On the choice of regularization matrix for an ℓ2-ℓq minimization method for image restoration Appl. Numer. Math. (IF 1.979) Pub Date : 2020-11-12 Alessandro Buccini; Guangxin Huang; Lothar Reichel; Feng Yin
Ill-posed problems arise in many areas of science and engineering. Their solutions, if they exist, are very sensitive to perturbations in the data. To reduce this sensitivity, the original problem may be replaced by a minimization problem with a fidelity term and a regularization term. We consider minimization problems of this kind, in which the fidelity term is the square of the ℓ2-norm of a discrepancy
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