In this paper, we develop and analyze a high order compact finite difference method (CFDM)
for solving a general class of two-point nonlinear singular boundary value problems with …

Up to tenth-order finite difference schemes are proposed in this paper to solve one-
dimensional advection-diffusion equation. The schemes based on high-order differences …

This study aims to produce numerical solutions of one‐dimensional advection‐diffusion
equation using a sixth‐order compact difference scheme in space and a fourth‐order Runge …

The term'optimization'refers to the process of maximizing the beneficial attributes of a
mathematical function or system while minimizing the unfavorable ones. The majority of real …

In this work, we use a reproducing kernel method for investigating the sine-Gordon equation
with initial and boundary conditions. Numerical experiments are studied to show the …

In this article, up to tenth‐order finite difference schemes are proposed to solve the
generalized Burgers–Huxley equation. The schemes based on high‐order differences are …

The purpose of this work is to propose a new composite scheme based on differential
quadrature method (DQM) and modified cubic unified and extended trigonometric B-spline …

Abstract In this paper, Crank-Nicolson differential quadrature method based on cubic
exponential B-spline (CExpB-spline) functions is presented to approximate the 1D nonlinear …

In this article, we study an explicit scheme for the solution of sine‐Gordon equation when the
space discretization is carried out by an overlapping multidomain pseudo‐spectral …

The present article is concerned with the implementation of the compact finite difference
scheme, in the space and the optimal four-stage, order three strong stability-preserving time …