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High-order nonstandard finite difference methods preserving dynamical properties of one-dimensional dynamical systems
In this work, we introduce a simple and efficient approach for constructing dynamically consistent and high-order nonstandard finite difference...
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On Finite Difference Jacobian Computation in Deformable Image Registration
Producing spatial transformations that are diffeomorphic is a key goal in deformable image registration. As a diffeomorphic transformation should...
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Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion
This paper proposes and analyzes a tempered fractional integrodifferential equation in three-dimensional (3D) space. The Crank-Nicolson (CN) method...
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A Nonstandard Finite Difference Method for a General Epidemic Model
This paper aims to investigate the qualitative properties of a general SIR model. The model includes a general function that describes the effect...
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A finite difference scheme for the two-dimensional Gray-Scott equation with fractional Laplacian
This paper studies numerical methods for the two-dimensional fractional Gray-Scott (GS) model with fractional Laplacian. A three-level linearized...
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Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime
We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless...
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Improved parallel finite element methods for the stationary Navier–Stokes problem
In this study, two improved parallel finite element algorithms based on two-grid strategies are developed to approximate the stationary Navier–Stokes...
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Optimal error estimates of penalty difference finite element method for the 3D steady Navier-Stokes equations
In this paper, a penalty difference finite element (PDFE) method is presented for the 3D steady Navier-Stokes equations by using the finite element...
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Scalable computational kernels for mortar finite element methods
Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite...
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Finite difference formulas in the complex plane
Among general functions of two variables f ( x , y ), analytic functions f ( z ) with z = x + i y form a very important special case. One consequence of...
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Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability
In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the...
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Mixed Finite Element Methods for the Navier–Stokes–Biot Model
We present two mixed finite element methods for the quasistatic Navier–Stokes–Biot model. The methods are based on a fully-mixed formulation, using...
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A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions
In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the...
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A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation
This paper is concerned with a linearized second-order finite difference scheme for solving the nonlinear time-fractional Schrödinger equation in d ( d ...
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Comparison of Finite Difference Schemes of Different Orders of Accuracy for the Burgers Wave Equation Problem
A large number of problems in physics and technology lead to boundary value or initial boundary value problems for linear and nonlinear partial...
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Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes
In this paper, we develop a polygonal mesh adaptation algorithm for a fully implicit scheme based on discontinuous Galerkin (DG) finite element...
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Optimal convergence analysis of weak Galerkin finite element methods for parabolic equations with lower regularity
This paper is devoted to investigating the optimal convergence order of a weak Galerkin finite element approximation to a second-order parabolic...
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An MP-DWR method for h-adaptive finite element methods
In a dual-weighted residual method based on the finite element framework, the Galerkin orthogonality is an issue that prevents solving the dual...
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High order hybrid asymptotic augmented finite volume methods for nonlinear degenerate wave equations
In this paper, we provide high order hybrid asymptotic augmented finite volume schemes on a uniform grid for nonlinear weakly degenerate and strongly...
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The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations
In this paper, four linearly energy-preserving finite difference methods (EP-FDMs) are designed for two-dimensional (2D) nonlinear coupled...
