An approximation method for electromagnetic wave models based on fractional partial derivative

TL;DR

This paper introduces a numerical method using Bernoulli and Hermite wavelets to solve fractional PDEs modeling electromagnetic waves in dielectric media, demonstrating high accuracy through numerical experiments.

Contribution

It develops a novel wavelet-based approximation technique for fractional PDEs in electromagnetic wave modeling, including convergence and error analysis.

Findings

Accurate solutions for fractional PDEs in electromagnetic media.

Effective wavelet-based discretization with convergence guarantees.

Numerical results closely match analytical solutions.

Abstract

The present article is devoting a numerical approach for solving a fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM). The truncated Bernoulli and Hermite wavelets series with unknown coefficients have been used to approximate the solution in both the temporal and spatial variables. The basic idea for discretizing the FPDE is wavelet approximation based on the Bernoulli and Hermite wavelets operational matrices of integration and differentiation. The resulted system of a linear algebraic equation has been solved by the collocation method. Moreover, convergence and error analysis have been discussed. Finally, several numerical experiments with different fractional-order derivatives have been provided and compared with the exact analytical solutions to illustrate the accuracy and efficiency of the method.