An implicit fully discrete compact finite difference scheme for time fractional diffusion-wave equation

Wenjing An; Xingdong Zhang; Wenjing An; Xingdong Zhang

doi:10.3934/era.2024017

Electronic Research Archive

2024, Volume 32, Issue 1: 354-369. doi: 10.3934/era.2024017

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Research article

An implicit fully discrete compact finite difference scheme for time fractional diffusion-wave equation

Wenjing An ^1,2,
Xingdong Zhang ^{2
,
,}

1.
Department of Normal Education, Xinjiang Applied Vocational Technical College, Kuitun 833200, China
2.
School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China

Received: 24 October 2023 Revised: 05 December 2023 Accepted: 12 December 2023 Published: 26 December 2023

In this paper, an implicit compact finite difference (CFD) scheme was constructed to get the numerical solution for time fractional diffusion-wave equation (TFDWE), in which the time fractional derivative was denoted by Caputo-Fabrizio (C-F) sense. We proved that the full discrete scheme is unconditionally stable. We also proved that the rate of convergence in time is near to $ O(\tau^{2}) $ and the rate of convergence in space is near to $ O(h^{4}) $. Test problem was considered for regular domain with uniform points to validate the efficiency and accuracy of the method. The numerical results can support the theoretical claims.
- time fractional diffusion-wave equation (TFDWE),
- compact finite difference,
- caputo-fabrizio derivative,
- unconditional stability,
- convergence
Citation: Wenjing An, Xingdong Zhang. An implicit fully discrete compact finite difference scheme for time fractional diffusion-wave equation[J]. Electronic Research Archive, 2024, 32(1): 354-369. doi: 10.3934/era.2024017

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Abstract

In this paper, an implicit compact finite difference (CFD) scheme was constructed to get the numerical solution for time fractional diffusion-wave equation (TFDWE), in which the time fractional derivative was denoted by Caputo-Fabrizio (C-F) sense. We proved that the full discrete scheme is unconditionally stable. We also proved that the rate of convergence in time is near to $ O(\tau^{2}) $ and the rate of convergence in space is near to $ O(h^{4}) $. Test problem was considered for regular domain with uniform points to validate the efficiency and accuracy of the method. The numerical results can support the theoretical claims.

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