Numerical analysis for the Klein-Gordon equation with mass parameter

Advances in Difference Equations

Badr Saad T Alkahtani¹  Ilknur Koca²  Abdon Atangana³ 

[1] Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia;Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, Burdur, Turkey;Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

关键词: second approximation of fractional derivative;    Klein-Gordon equation;    stability analysis;   

DOI  :  10.1186/s13662-017-1352-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A numerical analysis of the well-known linear partial differential equation describing the relativistic wave is presented in this work. Three different operators of fractional differentiation with power law, exponential decay law and Mittag-Leffler law are employed to extend the Klein-Gordon equation with mass parameter to the concept of fractional differentiation. The three models are solved numerically. The stability and the convergence of the numerical schemes are investigated in detail.

【 授权许可】

CC BY