Telegraph equation with time Riesz space-fractional derivative approximated by Haar wavelets

Theory of Approximation and Applications

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 آبان 1402

نوع مقاله: Research Articles

نویسندگان

Yaghoub Mahmoudi^* ؛ Zeynab Abdollahy

Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

چکیده

In this study, one explicit and one implicit finite difference
scheme is introduced for the numerical solution of time-fractional Riesz
space diffusion equation. The time derivative is approximated by the standard Gr¨unwald Letnikov formula of order one, while the Riesz space derivative is discretized by Fourier transform-based algorithm of order four.
The stability and convergence of the proposed methods are studied. It
is proved that the implicit scheme is unconditionally stable, while the explicit scheme is stable conditionally. Some examples are solved to illustrate
the efficiency and accuracy of the proposed methods. Numerical results
confirm that the accuracy of present schemes is of order one.

کلیدواژه‌ها

Fractional derivatives؛ Haar wavelets؛ Telegraph equation؛ Riesz fractional derivative