Work

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

Year: 2023

Type: article

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 $ \alpha $ while $ 1 < \alpha < 2 $. The suggested methodology is developed from the standard five-points difference Crank-Nicolson S(FPCN) scheme by rotating clockwise $ 45^{o} $ 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.

Source: AIMS Mathematics

DOI: 10.3934/math.2023416

Authors: Ajmal Ali, Tayyaba Akram, Azhar Iqbal, Poom Kumam, Thana Sutthibutpong

Institutions: Virtual University of Pakistan, King Mongkut's University of Technology Thonburi, Prince Mohammad bin Fahd University, China Medical University, Center of Excellence in Theoretical and Computational Science

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Thailand Science Research and Innovation