Comparing Solutions to the Nonlinear Dissipative Wave Equation
Comparing Solutions to the Nonlinear Dissipative Wave Equation作者机构：Department of Mathematics College of Science and Arts King Khalid University Muhayil Asir KSA Mathematics College of Engineering & Science Victoria University Melbourne Australia Department of Mathematics Faculty of Sciences and Arts Taibah University Medina KSA
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2022年第10卷第4期
页 面：1281-1296页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Dissipative Wave Equation Cubic B-Spline Non-Polynomial Spline Truncation Error Von Neumann Stability
摘 要：In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One of these nonlinear partial differential equations, the dissipative wave equation, has been found to have a plethora of useful applications in different fields. A special class of solutions has been studied for the dissipative wave equation including exact solutions and approximate solutions. The aim of this article is to compare the non-polynomial spline method and the cubic B-spline method with the solution of a nonlinear dissipative wave equation. We will conduct a comparison of the stability of the two methods using the Von Neumann stability analysis. In addition, a numerical example will be presented to illustrate the accuracy of these methods.
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