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

Ajmal Ali; Tayyaba Akram; Azhar Iqbal; Poom Kumam; Thana Sutthibutpong; Ajmal Ali; Tayyaba Akram; Azhar Iqbal; Poom Kumam; Thana Sutthibutpong

doi:10.3934/math.2023416

AIMS Mathematics

2023, Volume 8, Issue 4: 8249-8273. doi: 10.3934/math.2023416

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Research article

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

1.
Department of Mathematics, Virtual University of Pakistan, Lahore 54000, Pakistan
2.
Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand
3.
Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia
4.
Center of Excellence in Theoretical and Computational Science & KMUTT Fixed Point Research Laboratory, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
6.
Theoretical and Computational Physics Group, Department of Physics, King Mongkut's University of Technology Thonburi, Bangkok, Thailand
7.
Center of Excellence in Theoretical and Computational Science Center, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand

Received: 17 October 2022 Revised: 12 December 2022 Accepted: 18 December 2022 Published: 01 February 2023
MSC : 65N06, 65M06, 65M12

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.
Citation: Ajmal Ali, Tayyaba Akram, Azhar Iqbal, Poom Kumam, Thana Sutthibutpong. A numerical approach for 2D time-fractional diffusion damped wave model[J]. AIMS Mathematics, 2023, 8(4): 8249-8273. doi: 10.3934/math.2023416

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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 $ \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.

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