Influence of the Forward Difference Scheme for the Time Derivative on the Stability of Wave Equation Numerical Solution

07/02/2018
by   Aslam Abdullah, et al.
0

Research on numerical stability of difference equations has been quite intensive in the past century. The choice of difference schemes for the derivative terms in these equations contributes to a wide range of the stability analysis issues - one of which is how a chosen scheme may directly or indirectly contribute to such stability. In the present paper, how far the forward difference scheme for the time derivative in the wave equation influences the stability of the equation numerical solution, is particularly investigated. The stability analysis of the corresponding difference equation involving four schemes, namely Lax's, central, forward, and rearward differences, were carried out, and the resulting stability criteria were compared. The results indicate that the instability of the solution of wave equation is not always due to the forward difference scheme for the time derivative. Rather, it is shown in this paper that the stability criterion is still possible when the spatial derivative is represented by an appropriate difference scheme. This sheds light on the degree of applicability of a difference scheme for a hyperbolic equation.

READ FULL TEXT
research
06/17/2019

Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative

In this paper, we investigate the numerical approximation of Hamilton-Ja...
research
04/27/2020

Stability theory for some scalar finite difference schemes : Validity of the modified equations approach

In this paper, we discuss some limitations of the modified equations app...
research
11/09/2021

Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory

We consider the Cauchy problem for a first-order evolution equation with...
research
09/07/2022

Convergence analysis of an implicit finite difference method for the inertial Landau-Lifshitz-Gilbert equation

The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fa...
research
01/16/2023

Convergence Analysis of the Upwind Difference Methods for Hamilton-Jacobi-Bellman Equations

The convergence properties of the upwind difference scheme for the Hamil...
research
12/15/2019

An improved Haar wavelet quasilinearization technique for a class of generalized Burger's equation

Solving Burgers' equation always poses challenge to researchers as for s...
research
03/17/2022

Numerical simulations of semi-linear Klein-Gordon equations in the de Sitter spacetime with structure preserving scheme

We perform some simulations of the Klein-Gordon equation in the de Sitte...

Please sign up or login with your details

Forgot password? Click here to reset