Numerical solutions of fractional wave equations using an efficient class of FDM based on the Hermite formula

Advances in Difference Equations

Mohamed M Khader¹  Mohamed H Adel² 

[1] Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia;Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

关键词: finite difference methods;    Hermite formula;    fractional wave equation;    stability and convergence analysis;   

DOI  :  10.1186/s13662-015-0731-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, a numerical study is introduced for solving the fractional wave equations by using an efficient class of finite difference methods. The proposed scheme is based on the Hermite formula. The stability and the convergence analysis of the proposed methods are given by a recently proposed procedure similar to the standard von Neumann stability analysis. A simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, are given and checked numerically. Finally, a numerical example is presented to confirm the theoretical results.

【 授权许可】

CC BY