In this paper, we study the stability of a numerical boundary treatment of high order compact finite difference methods for parabolic equations. The compact finite difference schemes could achieve very high order accuracy with relatively small stencils. To match the convergence order of the compact schemes in the interior domain, we take the simplified inverse Lax–Wendroff (SILW) procedure (Tan et

In this paper the problem of Synthetic Aperture Radar (SAR) and optical satellite images co-registration is considered. Because of the distinct natures of SAR and optical images, there exist huge radiometric and geometric differences between such images. As a result, the traditional registration approaches are no longer applicable in this case and it makes the registration process challenging. Mostly

In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. While intrusive methods inherit certain advantages such as adaptivity and an improved accuracy, they suffer from two key issues. First, intrusive methods tend to show oscillations, especially at shock structures and second, standard intrusive methods can lose hyperbolicity. The aim

We study the problem of minimizing the first eigenvalue of the p-Laplacian operator for a two-phase material in a bounded open domain Ω⊂RN, N⩾2 assuming that the amount of the best material is limited. We provide a relaxed formulation of the problem and prove some smoothness results for these solutions. As a consequence we show that if Ω is of class C1,1, simply connected with connected boundary, then

Discontinuous Galerkin composite finite element methods (DGCFEM) are designed to tackle approximation problems on complicated domains. Partial differential equations posed on complicated domain are common when there are mesoscopic or local phenomena which need to be modeled at the same time as macropscopic phenomena. In this paper, an optical lattice will be used to illustrate the performance of the

Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe–Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab initio), i.e. without the need for empirical data in the model. To harness the predictive power of the equation, it is mapped to an eigenvalue problem via an appropriate

A new heuristic parameter choice rule is proposed, which is an important process in solving the linear ill-posed integral equation. Based on multiscale Galerkin projection, we establish the error upper bound between the approximate solution obtained by this rule and the exact solution. Under certain condition, we prove that the approximate solution obtained by this rule can reach the optimal convergence

Based on the absolute value equation for minimizing two vectors, we present error bounds for the linear complementarity problems with an H+-matrix. Some of the computable bounds are given by providing the particular diagonal parameter matrix D. The proposed bounds improve some existing ones when D is chosen properly.

In this work, we consider multidimensional diffusion-reaction equations with time-fractional partial derivatives of the Caputo type and orders of differentiation in (0,1). The models are extensions of various well-known equations from mathematical physics, biology, and chemistry. In the present manuscript, we will impose initial–boundary data on a closed and bounded spatial multidimensional domain

This paper proposes a class of randomized Kaczmarz algorithms for obtaining isolated solutions of large-scale well-posed or overdetermined nonlinear systems of equations. This type of algorithm improves the classic Newton method. Each iteration only needs to calculate one row of the Jacobian instead of the entire matrix, which greatly reduces the amount of calculation and storage. Therefore, these

Jacobian-free Newton–Krylov (JFNK) method is a popular approach to solve nonlinear algebraic equations arising from computational physics. The key issue is the calculation of Jacobian-vector product, commonly done through finite difference methods. However, these approaches suffer from both truncation error and round-off error, and the accuracy heavily depends on a sophisticated choice of the difference

We investigate a quasi-static tensile fracture in nonlinear strain-limiting solids by coupling with the phase-field approach. A classical model for the growth of fractures in an elastic material is formulated in the framework of linear elasticity for deformation systems. This linear elastic fracture mechanics (LEFM) model is derived based on the assumption of small strain. However, the boundary value

In this paper, we propose a modified SOR-like method for solving absolute value equations associated with second order cones (SOCAVE in short), which is obtained by reformulating the SOCAVE as a two-by-two block nonlinear equation. The convergence analysis and error estimation of this method are established under mild assumptions on system matrix and iteration parameters. And, the optimal iteration

In this paper we formulate the convergence rates of the iteratively regularized Gauss–Newton method by defining the iterates via convex optimization problems in a Banach space setting. We employ the concept of conditional stability to deduce the convergence rates in place of the well known concept of variational inequalities. To validate our abstract theory, we also discuss an ill-posed inverse problem

The main purpose of this work is to study the numerical solution of a time fractional partial integro-differential equation of Volterra type, where the time derivative is defined in Caputo sense. Our method is a combination of the classical L1 scheme for temporal derivative, the general second order central difference approximation for spatial derivative and the repeated quadrature rule for integral

This paper deals with development and analysis of a finite volume (FV) method for the coupled system describing immiscible compressible two-phase flow, such as water-gas, in porous media, capillary and gravity effects being taken into account. We investigate a fully coupled fully implicit cell-centered “phase-by-phase” FV scheme for the discretization of such system. The main goal is to incorporate

We study efficient implicit methods to denoise low-field MR images using a nonlinear diffusion operator as a regularizer. This problem can be formulated as solving a nonlinear reaction–diffusion equation. After discretisation, a lagged-diffusion approach is used which requires a linear system solve in every nonlinear iteration. The choice of diffusion model determines the denoising properties, but

Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of freedom and, at the same time, for a more efficient engineering analysis. Moreover they possess a set of basis functions with similar properties to standard B-splines

The Arnoldi method is a commonly used technique for finding a few eigenpairs of large, sparse and nonsymmetric matrices. Recently, a new variant of Arnoldi method (NVRA) was proposed. In NVRA, the modified Ritz vector is used to take the place of the Ritz vector by solving a minimization problem. Moreover, it was shown that if the refined Arnoldi method converges, then the NVRA method also converges

Method of optimizing the distance between individual elements in the antenna array is presented. Based on the verification of the analytical model for one defined rectangular patch antenna and subsequently for the antenna array, the sweep analysis was performed for variant voltage and phase values on each element of the array. The results were used as the input parameters for creating a surrogate model

In this paper, a new approach, the Variance Gamma (VG) model, which is used to capture unexpected shocks (e.g., Covid-19) in housing markets, is proposed to contribute to the standard option-based mortgage valuation methods. Based on the VG model, the closed-form solutions are performed for pricing mortgage default and prepayment options. It solves the options pricing equations explicitly and illustrates

We propose and analyze a high order unfitted hybridizable discontinuous Galerkin method to numerically solve Oseen equations in a domain Ω having a curved boundary. The domain is approximated by a polyhedral computational domain not necessarily fitting Ω. The boundary condition is transferred to the computational domain through line integrals over the approximation of the gradient of the velocity and

Tridiagonal matrix inversion is an important operation with many applications. It arises frequently in solving discretized one-dimensional elliptic partial differential equations, and forms the basis for many algorithms for block tridiagonal matrix inversion for discretized PDEs in higher-dimensions. In such systems, this operation is often the scaling bottleneck in parallel computation. In this paper

The Bernstein operators (BO) are not orthogonal, but they have duals, which are obtained by a linear combination of BO. In recent years dual BO have been adopted in computer graphics, computer aided geometric design, and numerical analysis. This paper presents a numerical method based on the Bernstein operational matrices to solve the time–space fractional convection–diffusion equation. A generalization

The time distributed-order diffusion-wave equation describes radial groundwater flow to or from a well. In the paper, an alternating direction implicit (ADI) Legendre–Laguerre spectral scheme is proposed for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain. The Gauss quadrature formula has a higher computational accuracy than the Composite Trapezoid formula

Accurate algorithms are proposed for approximation of integrals involving highly oscillatory Bessel function of the first kind over finite and infinite domains. Accordingly, Bessel oscillatory integrals having high oscillatory behavior are transformed into oscillatory integrals with Fourier kernel by using complex line integration technique. The transformed integrals contain an inner non-oscillatory

The Hénon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We discuss a numerical verification method for proving the existence of solutions

In this article, we develop a residual-driven adaptive Gaussian mixture approximation (RD-AGMA) for Bayesian inverse problems. The posterior distribution is often non-Gaussian in practical Bayesian inference. To obtain a good approximation of the posterior, we provide the adaptive Gaussian mixture approximation (GMA) based on a residual. For GMA, the clustering of ensemble samples provides the predictor

In this paper, we study the finite-time ruin problems in the spectrally negative Lévy risk models. Suppose that the surplus process of an insurance company is observed periodically in a finite-time interval, and ruin is declared as soon as the observed surplus level is negative. A finite-time Gerber–Shiu expected discounted penalty function is studied. After approximating the common density function

Convection enhanced drug delivery (CED) is a technique used to make therapeutic agents reach, through a catheter, sites of difficult access. The name of this technique comes from the convective flow originated by a pressure gradient induced at the tip of the catheter. This flow enhances passive diffusion and allows a more efficient spread of the agents by the target site. CED is particularly useful

A new approach to the study of multidimensional singularly perturbed problems of nonlinear heat conduction is proposed, based on the further development and use of asymptotic analysis methods. We study the question of the existence of classical Lyapunov stable stationary solutions with boundary and internal transition layers (stationary thermal structures) of the nonlinear heat transfer equation. We

In the paper, we proposed an approach for studying strong and weak extremums in non-smooth vector problems of calculus of variation, namely, in classic variational problems with fixed ends and with a free right end, and also in a variational problem with higher derivatives. The essence of the proposed approach is to introduce a Weierstrass type variation characterized by a numerical parameter. Necessary

In this paper we introduce a hybrid absorbing boundary condition (HABC) by combining perfectly matched layer (PML) and complete radiation boundary condition (CRBC) for solving a one-dimensional diffraction grating problem. The new boundary condition is devised in such a way that it can enjoy relative advantages from both methods. The well-posedness of the problem with HABC and the convergence of approximate

The study of planar and spherical geometric subdivision schemes was done in Dyn and Hormann (2012); Bellaihou and Ikemakhen (2020). In this paper we complete this study by examining the hyperbolic case. We define general interpolatory geometric subdivision schemes generating curves on the hyperbolic plane by using geodesic polygons and the hyperbolic trigonometry. We show that a hyperbolic interpolatory

We introduce a tamed exponential time integrator which exploits linear terms in both the drift and diffusion for Stochastic Differential Equations (SDEs) with a one sided globally Lipschitz drift term. Strong convergence of the proposed scheme is proved, exploiting the boundedness of the geometric Brownian motion (GBM) and we establish order 1 convergence for linear diffusion terms. In our implementation

In this paper, we introduce fully implementable, adaptive Euler–Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz continuity in the state variable for either, while global Lipschitz continuity is required for the measure component only. We prove moment stability

The positive definiteness of an even degree homogeneous polynomial plays an important role in the stability study of nonlinear autonomous systems via Lyapunov’s direct method in automatic control, the detection of P or P0 tensor in tensor complementarity problems and spectral hypergraph theory, and more. Owing to the positive definiteness of an even degree homogeneous polynomial is equivalent to that

This paper deals with the application of fuzzy Mellin transform for fuzzy valued functions. It is an attempt to investigate fuzzy Mellin transform in fractional sense and called fuzzy fractional Mellin transform. Some techniques are proposed for the solution of fuzzy fractional order differential equations by using left-sided Riemann–Liouville fractional derivative. Moreover, some illustrative examples

In this paper, we study local and nonlocal boundary value problems for hyperbolic equations of general form with variable coefficients and a Caputo fractional derivative. To study the stated problem, a certain fractional-order functional space is introduced. The problem posed is reduced to an integral equation, and the existence of its solution is proved using an a priori estimate.

The challenge of estimating a population size (N) is usually faced with the well-established mark-recapture sampling scheme. The basic idea is to tag t items of the population and then observe the number of tagged items appearing in a subsequent random sample. The frequencies of tagged versus non-tagged items are informative to estimate N. For construction of fixed-width and fixed-accuracy confidence

This paper proposes the study of a newer class of integro-differential operators, which allow analysing a more general family of dynamical systems, with not necessarily integer-order differentiable solutions, and based on Volterra integral equations of the second kind. One of the main advantages of the present study is that the proposed operators include, in particular cases, some classical and modern

A well-known result in linear approximation theory states that the norm of the operator, known as the Lebesgue constant, of polynomial interpolation on an interval grows only logarithmically with the number of nodes, when these are Chebyshev points. Results like this are important for studying the conditioning of the approximation. A cosine change of variable shows that polynomial interpolation at

UE-splines are generalizations of uniform polynomial splines, trigonometric splines, hyperbolic splines and exponential splines defined as parametric splines in non-rational form. At the same time, they can exactly represent a wide class of basic analytic shapes commonly used in engineering applications. Further, UE-splines with uniform knot intervals can be conveniently generated by subdivision methods

In this paper, we consider numerical approximation to periodic measure of a time periodic stochastic differential equations (SDEs) under weakly dissipative condition. For this we first study the existence of the periodic measure ρt and the large time behaviour of U(t+s,s,x)≔Eϕ(Xts,x)−∫ϕdρt, where Xts,x is the solution of the SDEs and ϕ is a test function being smooth and of polynomial growth at infinity

It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a singularity close to the convex hull of the support of the measure. This paper investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of

This paper proposes an efficient localized meshless technique for approximating the viscoelastic wave model. This model is a significant methodology to explain wave propagation in solids modeled with a wide collection of viscoelastic laws. In the first method, a difference scheme with the second-order accuracy is implemented to obtain a semi-discrete scheme. Then, a localized radial basis function

Spatial generalized linear mixed models are commonly employed for modeling discrete spatial responses that are acquired on a continuous area. A standard assumption in these models is that the latent variables are normally distributed, however skewed residuals appear in some spatial generalized linear mixed models. In this study, we consider a closed skew Gaussian random field for the spatial latent

In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric matrices. As by-products, the generalizations of the filtered Krylov subspace method and the Chebyshev–Davidson method for solving non-symmetric eigenvalue problems

In this paper, we investigate nonlinear functional Volterra–Urysohn integral equations, a class of nonlinear integral equations of Volterra type. The existence and uniqueness of the solution to the equation is proved by a technique based on the Picard iterative method. For the numerical approximation of the solution, the Euler and trapezoidal discretization methods are utilized which result in a system

The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them with a small imaginary step next to the real number line. The current paper proposes that derivatives of holomorphic functions can be calculated in a similar fashion by taking a small step in a quaternionic direction instead. It is demonstrated

We study a defined contribution pension system with the return of premium clauses, which is embedded with two administrative fees: the charge on balance and the charge on flow. The fund wealth is invested in financial market with a riskless asset and a risky asset modeled by a constant elasticity of variance process. We use the Weibull model to characterize the force of mortality. The dynamic programming

A certain type of queueing system that is quite common in manufacturing systems occurs when the time between the arrivals of items approximately follows an exponential distribution with rate λ, the services are mechanized and their times may be considered approximately constant (b). In Kendall notation, such a queueing system is well known as an M∕D∕1 queue; despite being one of the simplest queueing

We propose a new generalized linear model for modeling multivariate events (N,X,Y), where N is the duration, X is the magnitude, and Y is the maximum of the event. Such events arise, for example, when a process is observed above or below a threshold. Examples include heat waves, flood, draught, or market growth or decline periods. The model is flexible to include different covariates for different

In recent years, in the literature of linear regression models, robust model selection methods have received increasing attention when the datasets contain even a small fraction of outliers. Outliers can have a serious impact on statistical inference and the choice of models using model selection criteria. Most of the existing robust information-based model selection methods are confined to robust

This paper studies the Eulerian–Lagrangian and Eulerian–Eulerian approaches for the simulation of interaction between free surface flow and particles. The dynamics of the fluid as well as the transport of the particles in the Eulerian description is solved using the lattice Boltzmann method. To minimize artificial diffusion in particle transport the lattice Boltzmann method with direction-dependent

In this study we apply a Kansa-radial basis function (RBF) collocation method to 2D and 3D boundary value problems (BVPs) governed by high order partial differential equations (PDEs) of order 2N where N∈N,N≥3. As in such problems there are N boundary conditions (BCs), N distinct sets of boundary centres are needed. These could all be placed on the boundary with each set being different to the other

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality of the probability space is relatively low. The time-dependent generalized polynomial chaos (TD-gPC) is one such technique that uses an evolving orthogonal basis

The tensor complementarity problem over circular cone (CCTCP for short) is studied, which is a specially structured nonlinear complementarity problem. Useful properties of the circular cone help to reformulate equivalently CCTCP as an implicit fixed-point equation. Based on the smoothing functions, we reformulate the obtained fixed-point equation as a family of parameterized smoothing equations. Moreover

We propose a new proximal alternating direction method of multipliers (ADMM) for solving a class of three-block nonconvex optimization problems with linear constraints. The proposed method updates the third primal variable twice per iteration and introduces semidefinite proximal terms to the subproblems with the first two blocks. The method can be regarded as an extension of the method proposed in

A methodology for finding unknown or unavailable parts of temperature-dependent material characteristics is presented. Knowledge of these parts is of great importance for solving problems connected with processing of metals at high temperatures where phase changes take place, such as welding or cladding. The paper presents a technique of calibration of these characteristics based on evaluation of experimentally