An efficient matrix approach for the numerical solutions of electromagnetic wave model based on fractional partial derivative

In this article, we construct an efficient numerical method by combining the matrix and Kronecker multiplication to solve a fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM). We adopted the operational matrix method (OMM) based on Bernoulli and Hermite wavelets for approximating the space and time derivatives. The proposed method transform FPDE into a system of an algebraic equation. For a better understanding of the method, numerical algorithms are also provided for the considered problems. Furthermore, the convergence of approximation and theoretical unconditional stability have been proved with respect to squire integrable norm. Finally, two numerical experiments with different fractional-order derivatives have been performed and compared with the analytical solutions to illustrate the accuracy and efficiency of the method. It is observed that the OMM is simple, easy to implement, yields highly accurate results at a small number of basis functions. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This article proposes an efficient numerical method combining matrix and Kronecker multiplication to solve a fractional partial differential equation arising from electromagnetic waves in dielectric media. The method transforms FPDE into an algebraic equation, and numerical algorithms and experiments are provided to demonstrate accuracy and efficiency. The simplicity and accuracy of the method make it highly effective with a small number of basis functions.