A numerical approach for 2D time-fractional diffusion damped wave model

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Publication Details

Author list: Ali, Ajmal; Akram, Tayyaba; Iqbal, Azhar; Kumam, Poom; Sutthibutpong, Thana;

Publisher: AIMS Press

Publication year: 2023

Volume number: 8

Issue number: 4

Start page: 8249

End page: 8273

Number of pages: 25

ISSN: 2473-6988

eISSN: 2473-6988

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85147652080&doi=10.3934%2fmath.2023416&partnerID=40&md5=ac8f180b622184a9b6c60bca5022ac99

Languages: English-Great Britain (EN-GB)

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Abstract

In this article, we introduce an approximation of the rotated five-point difference Crank-Nicolson R(FPCN) approach for treating the second-order two-dimensional (2D) time-fractional diffusion-wave equation (TFDWE) with damping, which is constructed from two separate sets of equations, namely transverse electric and transverse magnetic phases. Such a category of equations can be achieved by altering second-order time derivative in the ordinary diffusion damped wave model by fractional Caputo derivative of order α while 1 < α < 2. The suggested methodology is developed from the standard five-points difference Crank-Nicolson S(FPCN) scheme by rotating clockwise 45o with respect to the standard knots. Numerical analysis is presented to demonstrate the applicability and feasibility of the R(FPCN) formulation over the S(FPCN) technique. The stability and convergence of the presented methodology are also performed. © 2023 the Author(s), licensee AIMS Press.

Keywords

fractional diffusion damped wave model, standard and rotated five-point Crank-Nicolson approximations