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A new fast algorithm for computing the mock-Chebyshev nodes Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-09 B. Ali Ibrahimoglu
Interpolation by polynomials on equispaced points is not always convergent due to the Runge phenomenon, and also, the interpolation process is exponentially ill-conditioned. By taking advantage of the optimality of the interpolation processes on the Chebyshev-Lobatto nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev nodes for polynomial interpolation. Mock-Chebyshev
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Computation of pairs of related Gauss-type quadrature rules Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-09 H. Alqahtani, C.F. Borges, D.Lj. Djukić, R.M. Mutavdžić Djukić, L. Reichel, M.M. Spalević
The evaluation of Gauss-type quadrature rules is an important topic in scientific computing. To determine estimates or bounds for the quadrature error of a Gauss rule often another related quadrature rule is evaluated, such as an associated Gauss-Radau or Gauss-Lobatto rule, an anti-Gauss rule, an averaged rule, an optimal averaged rule, or a Gauss-Kronrod rule when the latter exists. We discuss how
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Highly efficient, robust and unconditionally energy stable second order schemes for approximating the Cahn-Hilliard-Brinkman system Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-08 Peng Jiang, Hongen Jia, Liang Liu, Chenhui Zhang, Danxia Wang
In this paper, we present an efficient, robust, and unconditionally energy stable second-order scheme for solving the Cahn-Hilliard-Brinkman (CHB) model, which mathematically describes multiphase flow in porous media. Solving the CHB model is significantly challenging due to its high coupling and nonlinearity. Here, we utilize the scalar auxiliary variable (SAV) method to handle the nonlinear term
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Implicitly linear Jacobi spectral-collocation methods for two-dimensional weakly singular Volterra-Hammerstein integral equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-06 Qiumei Huang, Huiting Yang
Weakly singular Volterra integral equations of the second kind typically have nonsmooth solutions near the initial point of the interval of integration, which seriously affects the accuracy of spectral methods. We present Jacobi spectral-collocation method to solve two-dimensional weakly singular Volterra-Hammerstein integral equations based on smoothing transformation and implicitly linear method
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Spectral-Galerkin method for second kind VIEs with highly oscillatory kernels of the stationary point Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-01 Haotao Cai
In this paper, we discuss an efficient spectral approach for solving a class of second kind VIEs with highly oscillatory kernels possessing the stationary point. First, we use one variable transform to convert the highly oscillatory problem into the long-time one, and then split the long-time problem into a linear system of integral equations by using a dilation approach. Next on each interval we study
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Regularization with two differential operators and its application to inverse problems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-01 Shuang Yu, Hongqi Yang
We introduce a regularization method with two differential operators for solving a linear ill-posed operator equation system. The existence and uniqueness of regularized solutions to the problem are derived. With an a priori as well as an a posteriori parameter choice strategy, convergence and convergence rates of the regularized solution are also obtained. As an application, we apply the regularization
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Numerical discretization for Fisher-Kolmogorov problem with nonlocal diffusion based on mixed Galerkin BDF2 scheme Appl. Numer. Math. (IF 2.8) Pub Date : 2024-03-01 J. Manimaran, L. Shangerganesh, M.A. Zaky, A. Akgül, A.S. Hendy
Nonlocal problems involving fourth-order terms pose several difficulties such as numerical discretization and its related convergences analysis. In this paper, the well-posedness of the extended Fisher-Kolmogorov equation with nonlocal diffusion is first analyzed using the Faedo-Galerkin technique and the classical compactness arguments. Moreover, we adopt a BDF2 scheme for time discretization and
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Stability and convergence of BDF2-ADI schemes with variable step sizes for parabolic equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-29 Xuan Zhao, Haifeng Zhang, Ren-jun Qi
In this paper we propose and analyze the alternating direction implicit (ADI) difference schemes in conjunction with the second order backward differentiation formula (BDF2) method with variable time step sizes for solving the two-dimensional parabolic equation. The spatial compact operators are also applied to construct high order ADI scheme. By using the discrete energy method and the positive definiteness
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A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-28 A.F. Hegarty, E. O'Riordan
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used as test functions in one coordinate direction and are combined with bilinear trial functions defined on a Shishkin mesh. The resulting numerical method is shown
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Optimal spectral Galerkin approximation for time and space fractional reaction-diffusion equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-27 A.S. Hendy, L. Qiao, A. Aldraiweesh, M.A. Zaky
A one-dimensional space-time fractional reaction-diffusion problem is considered. We present a complete theory for the solution of the time-space fractional reaction-diffusion model, including existence and uniqueness in the case of using the spectral representation of the fractional Laplacian operator. An optimal error estimate is presented for the Galerkin spectral approximation of the problem under
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Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-22 Xinwu Liu, Ting Sun
To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the plus data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the fidelity is adopted to suppress Gaussian noise, while the -norm is more suitable for detecting and removing impulse
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An explicit substructuring method for overlapping domain decomposition based on stochastic calculus Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-21 Jorge Morón-Vidal, Francisco Bernal, Atsushi Suzuki
In a recent paper , a hybrid supercomputing algorithm for elliptic equations has been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques, such as the Schur complement method for the skeleton
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Finite element analysis of extended Fisher-Kolmogorov equation with Neumann boundary conditions Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Ghufran A. Al-Musawi, Akil J. Harfash
This paper delves into the numerical analysis of the extended Fisher-Kolmogorov (EFK) equation within open bounded convex domains , where . Two distinct finite element schemes are introduced, namely the semi-discrete and fully-discrete finite element approximations. The existence and uniqueness of solutions are established for both the semi-discrete and fully-discrete finite element approximations
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Adaptive H-matrix computations in linear elasticity Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Maximilian Bauer, Mario Bebendorf
This article deals with the efficient numerical treatment of the Lamé equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM). Using BEM, one is faced with the solution of a system of equations with a fully populated system matrix, which is in general very costly. In order to overcome this difficulty
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Monte Carlo method for the Cauchy problem of fractional diffusion equation concerning fractional Laplacian Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Caiyu Jiao, Changpin Li
In this paper, we study a Cauchy problem of fractional diffusion equation concerning fractional Laplacian. We prove the existence and uniqueness of solution to the problem under investigation in Hölder space. Then we apply the Monte Carlo method to solving this Cauchy problem. For the problem with free force term, we derive an unbiased scheme which only produces the statistic error. For the problem
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A discrete-ordinate weak Galerkin method for radiative transfer equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-15 Maneesh Kumar Singh
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting semi-discrete hyperbolic system is approximated using the weak Galerkin method. The stability result for the proposed numerical method is devised. A error analysis is
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Difference potentials method for the nonlinear convection-diffusion equation with interfaces Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-14 Mahboubeh Tavakoli Tameh, Fatemeh Shakeri
In this paper, the difference potentials method-based ADI finite difference scheme is proposed for numerical solutions of two-dimensional nonlinear convection–diffusion interface problems. We employ the Adams–Bashforth method to discretize nonlinear convection terms and the Crank-Nicolson method to discretize diffusion terms. Also, we use radial basis functions (RBF) to approximate the Cauchy data
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Efficient numerical methods for semilinear one dimensional parabolic singularly perturbed convection-diffusion systems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-13 C. Clavero, J.C. Jorge
In this work we deal with the numerical solution of one dimensional semilinear parabolic singularly perturbed systems of convection-diffusion type. We assume that the coupling in the convection terms is weak and also that the coupling reaction terms are nonlinear. In the case of considering different small diffusion parameters at each equation with different orders of magnitude, the exact solution
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Fast multi-level iteration schemes with compression technique for eigen-problems of compact integral operators Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-12 Guangqing Long, Huanfeng Yang, Dongsheng Cheng
In this paper, we present multi-level iteration schemes to solve the eigen-problems of compact integral operators based on the multiscale Galerkin methods. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique results in a fast algorithm. To further minimize computational complexity, we establish Jacobi, Gauss-Seidel and L-H iteration schemes for
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A penalty-type method for solving inverse optimal value problem in second-order conic programming Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-09 Yue Lu, Zheng-Peng Dong, Zhi-Qiang Hu, Hong-Min Ma, Dong-Yang Xue
This paper aims to consider a type of inverse optimal value problem in second-order conic programming, in which the parameter in its objective function needs to be adjusted under a given class that makes the corresponding optimal objective value closest to a target value. This inverse problem can be reformulated as a minimization problem with some second-order cone complementarity constraints. To tackle
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Numerical methods in modeling with supersaturated designs Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-09 N. Koukoudakis, C. Koukouvinos, A. Lappa, M. Mitrouli, A. Psitou
The present study aims to investigate the application of several numerical methods in least square problems, when the design matrix is a supersaturated design. This kind of statistical modeling appears frequently in a majority of applications and experiments where the main scope concerns the identification of the appropriate active factors and possible interactions as well. Several real data sets are
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An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-08 Ali Ugur Sazaklioglu
The main aims of this paper are to investigate the existence and uniqueness results for the solution of an inverse source problem for a multidimensional, semilinear, backward parabolic equation, subject to Dirichlet boundary conditions, and to propose an iterative difference scheme for the numerical solution of the problem. The unique solvability of the difference scheme is established, as well. In
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An asymptotic preserving and energy stable scheme for the Euler-Poisson system in the quasineutral limit Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-30 K.R. Arun, Rahuldev Ghorai, Mainak Kar
An asymptotic preserving (AP) and energy stable scheme for the Euler-Poisson (EP) system under the quasineutral scaling is designed and analysed. Appropriate stabilisation terms are introduced in the convective fluxes of mass and momenta, and the gradient of the electrostatic potential which lead to the dissipation of mechanical energy and consequently the entropy stability of solutions. The time discretisation
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Anderson acceleration. Convergence analysis and applications to equilibrium chemistry Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-02 Rawaa Awada, Jérôme Carrayrou, Carole Rosier
In this paper, we study theoretically and numerically the Anderson acceleration method. First, we extend the convergence results of Anderson's method for a small depth to general nonlinear cases. More precisely, we prove that the Type-I and Type-II Anderson(1) are locally q-linearly convergent if the fixed point map is a contraction with a Lipschitz constant small enough. We then illustrate the effectiveness
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An explicit Fourier-Klibanov method for an age-dependent tumor growth model of Gompertz type Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-02 Nguyen Thi Yen Ngoc, Vo Anh Khoa
This paper proposes an explicit Fourier-Klibanov method as a new approximation technique for an age-dependent population PDE of Gompertz type in modeling the evolution of tumor density in a brain tissue. Through suitable nonlinear and linear transformations, the Gompertz model of interest is transformed into an auxiliary third-order nonlinear PDE. Then, a coupled transport-like PDE system is obtained
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On the growth factor of Hadamard matrices of order 20 Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Emmanouil Lardas, Marilena Mitrouli
The aim of this work is to provide a complete list of all the possible values that the first six pivots of an Hadamard matrix of order 20 can take. This is accomplished by determining the possible values of certain minors of such matrices, in combination with the fact that the pivots can be computed in terms of these minors. We extend known results, by giving a different proof for the complete list
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A new class of symplectic methods for stochastic Hamiltonian systems Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Cristina Anton
We propose a systematic approach to construct a new family of stochastic symplectic schemes for the strong approximation of the solution of stochastic Hamiltonian systems. Our approach is based both on B-series and generating functions. The proposed schemes are a generalization of the implicit midpoint rule, they require derivatives of the Hamiltonian functions of at most order two, and are constructed
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Iterative method for constrained systems of conjugate transpose matrix equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Akbar Shirilord, Mehdi Dehghan
This study presents some new iterative algorithms based on the gradient method to solve general constrained systems of conjugate transpose matrix equations for both real and complex matrices. In addition, we analyze the convergence properties of these methods and provide numerical techniques to determine the solutions. The effectiveness of the proposed iterative methods is demonstrated through various
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Krylov subspace methods for large multidimensional eigenvalue computation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-02-01 Anas El Hachimi, Khalide Jbilou, Ahmed Ratnani
In this paper, we describe some Krylov subspace methods for computing eigentubes and eigenvectors (eigenslices) for large and sparse third-order tensors. This work provides projection methods for computing some of the largest (or smallest) eigentubes and eigenslices using the t-product. In particular, we use the tensor Arnoldi's approach for the non-hermitian case and the tensor Lanczos's approach
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A positivity-preserving well-balanced wet-dry front reconstruction for shallow water equations on rectangular grids Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 Xue Wang, Guoxian Chen
In this paper, a positivity-preserving, well-balanced finite volume scheme on a rectangular mesh is designed based on wet-dry front reconstruction to solve the shallow water equations with non-flat bottom topography. The crucial step is a special piecewise linear representation of the bottom. The flat bottom approximation simplifies the reconstruction of the wet-dry front, which becomes a straight
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Efficient Estimates for Matrix-Inverse Quadratic Forms Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 Emmanouil Bizas, Marilena Mitrouli, Ondřej Turek
In this paper we present two approaches for estimating matrix-inverse quadratic forms xTA−1x, where A is a symmetric positive definite matrix of order n, and x∈Rn. Using the first, analytic approach, we establish two families of estimates which are convenient for matrices with small condition number. Based on the second, heuristic approach, we derive two families of estimates which are suitable for
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A rank-updating technique for the Kronecker canonical form of singular pencils Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 Dimitrios Christou, Marilena Mitrouli, Dimitrios Triantafyllou
For a linear time-invariant system x˙(t)=Ax(t)+Bu(t), the Kronecker canonical form (KCF) of the matrix pencil (sI−A|B) provides the controllability indices, also called column minimal indices, of the system and their sum corresponds to the dimension of the controllable subspace. In this paper we introduce a fast numerical algorithm for computing the sets of column/row minimal indices of a singular
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A space-time Petrov-Galerkin method for the two-dimensional regularized long-wave equation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-22 Zhihui Zhao, Hong Li, Wei Gao
In this work, a space-time Petrov-Galerkin (STPG) method is used to numerically analyze the two-dimensional regularized long-wave (RLW) equation. The STPG method is a nonstandard finite element method, that is, both of the spatial and temporal variables of this method are discretized by finite element method. Therefore, it can display the superiority of the finite element method in both spatial and
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A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-23 E. Zampa, S. Busto, M. Dumbser
We present a novel semi-implicit hybrid finite volume/finite element (FV/FE) method for the equations of viscous and resistive incompressible magnetohydrodynamics (MHD). The scheme preserves the divergence-free property of the magnetic field exactly on the discrete level, is second order accurate in space, and is stable in the limit of vanishing viscosity and resistivity. In particular, the MHD system
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Collocation and modified collocation methods for solving second kind Fredholm integral equations in weighted spaces Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-18 Chafik Allouch
For the numerical solution of Fredholm integral equations on [−1,1] whose integrands have endpoint algebraic singularities, we investigate in this paper a modified collocation method based on the zeros of the Jacobi polynomials in appropriate weighted spaces. The proposed method converges faster than the standard collocation scheme, and the Sloan iteration can be used to make the solution even more
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Computational modeling of early-stage breast cancer progression using TPFA method: A numerical investigation Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-18 Manal Alotaibi, Françoise Foucher, Moustafa Ibrahim, Mazen Saad
In this paper, a finite volume (TPFA) method is employed to simulate a degenerate breast cancer model that captures the progressive mutations from a normal breast stem cell to a tumor cell. The model incorporates a degenerate parabolic equation to represent the interaction between solid tumor growth and its environment, which involves the release of degradative enzymes governed by a partial differential
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A symmetric and coercive finite volume scheme preserving the discrete maximum principle for anisotropic diffusion equations on star-shaped polygonal meshes Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-18 Shuai Su, Jiming Wu
A nonlinear vertex-centered finite volume scheme that preserves the discrete maximum principle (DMP) is proposed for anisotropic diffusion equations on polygonal meshes. The new scheme is constructed from a vertex-centered linearity-preserving scheme combined with a nonlinear correction technique. The key ingredient is the introduction of the correction coefficient and the limiter. Particularly, the
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The logarithmic truncated EM method with weaker conditions Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-18 Yiyi Tang, Xuerong Mao
In 2014, Neuenkirch and Szpruch established the drift-implicit Euler-Maruyama method for a class of SDEs which take values in a given domain. However, expensive computational cost is required for implementation of an implicit numerical method. A competitive positivity preserving explicit numerical method for SDEs which take values in the positive domain is the logarithmic truncated Euler-Maruyama method
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Some notes on the trapezoidal rule for Fourier type integrals Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-11 Eleonora Denich, Paolo Novati
This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the number of nodes can be a priori selected. The analysis is also used to design an automatic integrator that can be employed without any knowledge of the function involved
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Sparse Approximation of Complex Networks Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-11 Omar De la Cruz Cabrera, Jiafeng Jin, Lothar Reichel
This paper considers the problem of recovering a sparse approximation A∈Rn×n of an unknown (exact) adjacency matrix Atrue for a network from a corrupted version of a communicability matrix C=exp(Atrue)+N∈Rn×n, where N denotes an unknown “noise matrix”. We consider two methods for determining an approximation A of Atrue: (i) a Newton method with soft-thresholding and line search, and (ii) a proximal
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Fast Alternating Fitting Methods for Trigonometric Curves for Large Data Sets Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-11 Alessandro Buccini, Fei Chen, Omar De la Cruz Cabrera, Lothar Reichel
This paper discusses and develops new methods for fitting trigonometric curves, such as circles, ellipses, and dumbbells, to data points in the plane. Available methods for fitting circles or ellipses are very sensitive to outliers in the data, and are time consuming when the number of data points is large. The present paper focuses on curve fitting methods that are attractive to use when the number
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Partitioned schemes for the blood solute dynamics model by the variational multiscale method Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-12 Yongshuai Wang, Zhenjiang Peng, Md. Abdullah Al Mahbub, Haibiao Zheng
In this paper, we consider a heterogeneous model of solute absorption processes by the arterial wall. This model is based on an advection-diffusion equation describing the solute dynamics in the vascular lumen, the convective field being provided by the blood velocity. A pure diffusive model coupled with this equation is considered for the solute dynamics inside the arterial wall. The two subdomains
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Unconditional energy-stable method for the Swift–Hohenberg equation over arbitrarily curved surfaces with second-order accuracy Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-11 Binhu Xia, Xiaojian Xi, Rongrong Yu, Peijun Zhang
This paper presents an unconditional energy-stable method for the Swift-Hohenberg equation over arbitrarily curved surfaces. We directly define the Laplace–Beltrami operator on the triangular mesh and its dual mesh, which are the discretizations of regular surface. The direct discretization method has several advantages including intrinsic geometry, convergence property, and mass conservation. A second-order
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Weak approximation schemes for SDEs with super-linearly growing coefficients Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-11 Yuying Zhao, Xiaojie Wang
We propose a new class of weak approximation schemes for stochastic differential equations with coefficients of suplinearly growth. Both the modified weak Euler schemes and the drift-implicit weak Euler scheme are studied. Under certain non-globally Lipschitz conditions, the proposed schemes are proved to have first-order convergence in the weak sense. Numerical experiments are included to confirm
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On the construction of diagonally implicit two–step peer methods with RK stability Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-03 M. Sharifi, A. Abdi, G. Hojjati
In this paper, diagonally implicit two–step peer methods for the numerical solution of initial value problems of order ordinary differential are divided into four types including the combination of explicit and implicit methods in a sequential or parallel environments. In this class of the methods, construction of implicit methods equipped with Runge–Kutta stability property together with A– or L–stability
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Weighted chained graphs and some applications Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-04 C. Fenu, L. Reichel, G. Rodriguez, Y. Zhang
This paper introduces weighted chained graphs, as well as minimal broadcasting and receiving sets, and investigates their properties. Both directed and undirected graphs are considered. The notion of central nodes is introduced both for weighted directed and undirected graphs. This notion is helpful for determining how quickly information can propagate throughout a graph. In particular, it is useful
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On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-04 Ioannis Iordanis, Christos Koukouvinos, Iliana Silou
In this paper, Latin Hypercube Sampling (LHS) method is compared as per its effectiveness in supervised machine learning procedures. Employing LHS saves computer's processing time and in conjunction with Latin hypercube design properties and space filling ability, is considered as one of the most advanced mechanisms in terms of sampling. Although more data usually deliver better results, when using
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Romanovski-Jacobi spectral schemes for high-order differential equations Appl. Numer. Math. (IF 2.8) Pub Date : 2024-01-03 Y.H. Youssri, M.A. Zaky, R.M. Hafez
We develop direct solution techniques for solving high-order differential equations with constant coefficients using the spectral tau method. The spatial approximation is based on Romanovski-Jacobi polynomials {Rnα,β(x)}n=0N with α>−1, β<−2N−α−1, x∈(0,∞) and n is the polynomial degree. Then, a hybrid approach combining the Romanovski-Jacobi tau method with the Romanovski-Jacobi collocation technique
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Central composite designs with three missing observations Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-29 K. Alanazi, S.D. Georgiou, C. Koukouvinos, S. Stylianou
In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. This work therefore investigates the impact of a three missing observation of them various design points: factorial, axial and center points, on the estimation and
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Hybrid mixed discontinuous Galerkin finite element method for incompressible miscible displacement problem Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-28 Jiansong Zhang, Yun Yu, Jiang Zhu, Maosheng Jiang
A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve the pressure and velocity equations, and a new hybrid mixed discontinuous Galerkin finite element procedure is constructed to solve the concentration equation with upwind technique
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Location, separation and approximation of solutions of nonlinear Hammerstein-type integral equations Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-20 J.A. Ezquerro, M.A. Hernández-Verón
From Newton's method, we construct a Newton-type iterative method that allows studying a class of nonlinear Hammerstein-type integral equations. This method is reduced to Newton's method if the kernel of the integral equation is separable and, unlike Newton's method, can be applied to approximate a solution if the kernel is nonseparable. In addition, from an analysis of the global convergence of the
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Modifying Kurchatov's method to find multiple roots of nonlinear equations Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-20 Alicia Cordero, Neus Garrido, Juan R. Torregrosa, Paula Triguero-Navarro
We present a modification of Kurchatov's iterative method in order to solve a nonlinear equation with multiple roots, that is, for approximating solutions with multiplicity greater than one. One of its principal advantages is that you do not have to know a priori the multiplicity of the root, since it does not appear in the iterative expression. In order to examine the behaviour of the proposed method
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Mixed approximation of nonlinear acoustic equations: Well-posedness and a priori error analysis Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-22 Mostafa Meliani, Vanja Nikolić
Accurate simulation of nonlinear acoustic waves is essential for the continued development of a wide range of (high-intensity) focused ultrasound applications. In this article, we explore mixed finite element formulations of classical strongly damped quasilinear models of ultrasonic wave propagation, the Kuznetsov and Westervelt equations. Such formulations allow simultaneous retrieval of the acoustic
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Discrete Legendre spectral projection-based methods for Tikhonov regularization of first kind Fredholm integral equations Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-21 Subhashree Patel, Bijaya Laxmi Panigrahi
In this paper, we apply the discrete Legendre Galerkin and multi-Galerkin methods to find the approximate solution of the Tikhonov regularized equation of the Fredholm integral equations of the first kind. We evaluate the error bounds for the approximate solutions with the exact solution in the infinity norm. We provide an a priori parameter choice strategy to find the convergence rates under the infinity
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Loewner integer-order approximation of MIMO fractional-order systems Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-21 Hassan Mohamed Abdelalim Abdalla, Daniele Casagrande, Wiesław Krajewski, Umberto Viaro
A state–space integer–order approximation of commensurate–order systems is obtained using a data–driven interpolation approach based on Loewner matrices. Precisely, given the values of the original fractional–order transfer function at a number of generalised frequencies, a descriptor–form state–space model matching these frequency response values is constructed from a suitable Loewner matrix pencil
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Variational multiscale stabilized finite element analysis of transient MHD Stokes equations with application to multiply driven cavity flow Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-21 Anil Rathi, Dipak Kumar Sahoo, B.V. Rathish Kumar
The transient Stokes magnetohydrodynamic (Stokes MHD) equations are thoroughly investigated in this paper using the variational subgrid multiscale stabilized finite element approach. In order to get the optimal order of convergence, appropriate stabilization parameter expressions have been derived using Fourier analysis. The theoretical convergence analysis of the subgrid algebraic stabilized numerical
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An augmented Lagrangian approach for cardinality constrained minimization applied to variable selection problems Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-19 N. Krejić, E.H.M. Krulikovski, M. Raydan
To solve convex constrained minimization problems, that also include a cardinality constraint, we propose an augmented Lagrangian scheme combined with alternating projection ideas. Optimization problems that involve a a cardinality constraint are NP-hard mathematical programs and typically very hard to solve approximately. Our approach takes advantage of a recently developed and analyzed continuous
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A new error estimates of finite element method for (2+1)-dimensional nonlinear advection-diffusion model Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-19 , Ram Jiwari
This paper designs, analyzes, and implements a finite element analysis for the simulation of the nonlinear advection-diffusion model. The key feature of the proposed work is to provide novel a priori error estimates in Bôchner norms L2(0,T;H01(Ω)) and L∞(0,T;H01(Ω)) simultaneously. To achieve the desired error estimates for both semidiscrete and fully discrete schemes, our idea is to introduce the
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An effective QLM-based Legendre matrix algorithm to solve the coupled system of fractional-order Lane-Emden equations Appl. Numer. Math. (IF 2.8) Pub Date : 2023-12-11 Mohammad Izadi, Dumitru Baleanu
The purpose of this study is to propose a computationally effective algorithm for the numerical evaluation of a fractional-order system of singular Lane-Emden type equations arising in physical problems. The fractional operator considered is in the sense of the Liouville-Caputo derivative. The presented matrix collocation method is based upon a combination of the quasilinearization method (QLM) and