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An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation
In this paper, a numerical method is presented to solve a nonlinear weakly singular time-fractional partial integro–differential equation with Caputo...
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Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative
In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard...
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Finite Difference Schemes of 4th Order Approximation for Maxwell’s Equations
AbstractIn this paper, optimal difference schemes for solving Maxwell’s equations using a Laquerre spectral transformation are considered. Additional...
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High-order finite difference methods
Finite difference (FD) methods are very popular for solving partial differential equations (PDEs) because of their simplicity. A simple but powerful...
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Wavelet-based approximation with nonstandard finite difference scheme for singularly perturbed partial integrodifferential equations
A non-standard finite difference scheme with Haar wavelet basis functions is constructed for the convection–diffusion type singularly perturbed...
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Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem
AbstractWe consider the solution of a two-phase miscible displacement problem on dynamic adaptive meshes using the mimetic finite difference method....
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Gaussian Beam Ansatz for Finite Difference Wave Equations
This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in...
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A Finite Difference Scheme for the Fractional Laplacian on Non-uniform Grids
In this study, we analyze the convergence of the finite difference method on non-uniform grids and provide examples to demonstrate its effectiveness...
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Temporal Second-Order Fast Finite Difference/Compact Difference Schemes for Time-Fractional Generalized Burgers’ Equations
Two kinds of numerical schemes are investigated for time-fractional generalized Burgers’ equations (TFGBE). The first kind is obtained by the...
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Meshfree Finite Difference Solution of Homogeneous Dirichlet Problems of the Fractional Laplacian
A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value...
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Compact finite difference schemes with high resolution characteristics and their applications to solve Burgers equation
In this article, non-standard compact finite difference schemes are constructed for the numerical approximation to first- and second-order...
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Finite Difference Methods: Construction and Implementation
In this chapter, we discuss a class of time-step** schemes of finite difference type, whose construction is based on polynomial interpolation: we...
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Compact Finite Difference Scheme for Euler–Bernoulli Beam Equation with a Simply Supported Boundary Conditions
In this paper, we develop a fourth-order compact finite difference method to numerically solve a fourth-order parabolic differential equation that...
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A fast finite difference method for 2D time variable fractional mobile/immobile equation
In this paper, we establish a fast Crank–Nicolson L1 finite difference scheme for two-dimensional time variable fractional mobile/immobile diffusion...
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Highly localized RBF Lagrange functions for finite difference methods on spheres
The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the sphere can be used to create a numerically feasible, stable...
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On the Accuracy of Finite-Difference Schemes in Calculations of Centered Rarefaction Waves
AbstractA comparative accuracy analysis of three finite-difference schemes (the first order UpWind (UW), the second order TVD, and the third order in...
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Higher-Order Finite-Difference Schemes for Nonlinear Two-Point Boundary Value Problems
We present a family of high-order multi-point finite difference methods for solving nonlinear two-point boundary value problems. The family involves...