Even if numerical simulation of the Burgers' equation is well documented in the literature, a
detailed literature survey indicates that gaps still exist for comparative discussion regarding …

The various studies of partial differential equations (PDEs) are hot topics of mathematical
research. Among them, solving PDEs is a very important and difficult task. Since many …

A novel fourth-order three-point compact operator for the nonlinear convection term uux is
provided in this paper. The operator makes the numerical analysis of higher-order difference …

This paper formulates a third-order backward differentiation formula (BDF3) fourth-order
compact difference scheme based on a developed fourth-order operator for computing the …

The main aim of the current paper is to propose an efficient numerical procedure based on
the meshless method for solving some models of conservation laws. In the current …

In this article, a hybrid numerical method based on Haar wavelets and finite differences is
proposed for shock ridden evolutionary nonlinear time‐dependent partial differential …

Abstract The Swift–Hohenberg (SH) energy functional has been widely used to study pattern
formation. The L 2-and H− 1-gradient flows for the SH energy functional are the SH and …

Fractional differential equations have been proved to be valuable tools for modeling
diffusive processes associated with anomalous diffusion or spatial heterogeneity. However …

We propose a new Eulerian-Lagrangian Runge-Kutta finite volume method for numerically
solving convection and convection-diffusion equations. Eulerian-Lagrangian and semi …

In this article, we are concerned with the numerical analysis of a nonlinear implicit difference
scheme for Burgers' equation. A priori estimation of the analytical solution is provided in the …