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An efficient finite difference scheme for fractional partial differential equation arising in electromagnetic waves model | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 16، دوره 14، شماره 10، دی 2023، صفحه 163-178 اصل مقاله (612.24 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28651.3962 | ||
| نویسنده | ||
| Vijay Kumar Patel* | ||
| School of Advanced Sciences and Languages, VIT Bhopal University, Bhopal, India | ||
| تاریخ دریافت: 20 مهر 1401، تاریخ بازنگری: 03 بهمن 1401، تاریخ پذیرش: 16 بهمن 1401 | ||
| چکیده | ||
| We present an unconditionally stable finite difference scheme (FDS) for the fractional partial differential equation (PDE) arising in the electromagnetic waves, which contains both initial and Dirichlet boundary conditions. The Riemann-Liouville fractional derivatives in time are discretized by a finite difference scheme of order $\mathcal{O}\left( \Delta t^{3-\alpha}\right)$ and $\mathcal{O}\left( \Delta t^{3-\beta}\right)$, $1<\beta < \alpha < 2$ and the Laplacian operator is discretized by central difference approximation. The proposed stable FDS schemes transform the fractional PDE into a tridiagonal system. Theoretically, uniqueness, unconditionally stability, error bound, and convergence of FDS are investigated. Moreover, the accuracy of the order of convergence $\mathcal{O}\left( \Delta t^{3-\alpha}+ \Delta t^{3-\beta}+\Delta x^2 \right)$ of the scheme is investigated. Finally, numerical results are reported to illustrate our optimal error bound, order of convergence, and efficiency of proposed schemes. | ||
| کلیدواژهها | ||
| Fractional PDE؛ Finite difference scheme؛ Reimann-Liouville fractional derivative؛ Convergence analysis | ||
| مراجع | ||
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