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Register a new userAn approximation method for electromagnetic wave models based on fractional partial derivative
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Added by
Vijay Kumar Patel
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Vijay Kumar Patel
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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.
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In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The numerical scheme is based on the Hermite formula. The Caputos fractional derivatives in time are discretized by a finite difference scheme of order $mathcal{O}(k^{(4-alpha)})$ & $mathcal{O}(k^{(4-beta)})$, $1<beta <alpha leq 2$. The stability and the convergence analysis of the proposed methods are given by a procedure similar to the standard von Neumann stability analysis under mild conditions. Also for FPDE, accuracy of order $mathcal{O}left( k^{(4-alpha)}+k^{(4-beta)}+h^2right) $ is investigated. Finally, several numerical experiments with different fractional-order derivatives are provided and compared with the exact solutions to illustrate the accuracy and efficiency of the scheme. A comparative numerical study is also done to demonstrate the efficiency of the proposed scheme.
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