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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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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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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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Finite Difference Time Domain Methods for the Dirac Equation Coupled with the Chern–Simons Gauge Field
We introduce finite difference time domain (FDTD) methods for solving the Dirac equation coupled with the Chern–Simons gauge field and provide their...
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On the Comparison of Two Meshless Finite Difference Methods for Solving Shallow Water Equations
In this article, we present a numerical analysis of the Korteweg-de Vries (KdV) and Regularized Long Wave (RLW) equations using a finite difference...
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Finite Difference Methods on Uniform Meshes
In this chapter, we provide an analysis of one representative time-step** scheme of finite difference type, i.e., L1 scheme, on uniform temporal...
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Error Estimates of Finite Difference Methods for the Biharmonic Nonlinear Schrödinger Equation
We present two finite difference time domain methods for the biharmonic nonlinear Schrödinger equation (BNLS) by reformulating it into a system of...
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Quadratic regularization methods with finite-difference gradient approximations
This paper presents two quadratic regularization methods with finite-difference gradient approximations for smooth unconstrained optimization...
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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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Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations
In this paper, two efficient, linearized (or semi-implicit) Crank-Nicolson block-centered finite difference algorithms for the strongly nonlinear...
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Maximum-Norm Error Estimates of Fourth-Order Compact and ADI Compact Finite Difference Methods for Nonlinear Coupled Bacterial Systems
In this paper, by introducing two temporal derivative-dependent auxiliary variables, a linearized and decoupled fourth-order compact finite...
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Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts
In this paper, exponentially fitted finite difference methods are presented for singularly perturbed one-dimensional parabolic partial differential...
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Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel
In this paper, we propose an efficient numerical algorithm for the solution of fourth-order time fractional partial integro-differential equation...
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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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Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations
The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear...
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Nonstandard Finite Difference Scheme for the Epidemic Model with Vaccination
For the epidemic model with vaccination we present a new nonstandard finite difference scheme by using an exponential integrator to discretize...
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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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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...
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High Order Finite Difference WENO Methods for Shallow Water Equations on Curvilinear Meshes
A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux...
