EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY

Emadidin Gahalla Mohmed Elmahdi; Jianfei Huang

doi:10.11948/20210444

2022 Volume 12 Issue 2

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Emadidin Gahalla Mohmed Elmahdi, Jianfei Huang. EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 831-849. doi: 10.11948/20210444

Citation:

Emadidin Gahalla Mohmed Elmahdi, Jianfei Huang. EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 831-849. doi: 10.11948/20210444

EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY

1.
College of Mathematical Sciences, Yangzhou University, 225002 Yangzhou, China
2.
Faculty of Education, University of Khartoum, P. O. Box 321 Khartoum, Sudan

Corresponding author: Email address: jfhuang@lsec.cc.ac.cn(J. Huang)
Fund Project: The authors were supported by Natural Science Foundation of Jiangsu Province of China (No. BK20201427) and by National Natural Science Foundation of China (Nos. 11701502 and 11871065)

Abstract

Abstract

In this paper, we present an efficient linearized alternating direction implicit (ADI) scheme for two-dimensional time-space fractional nonlinear diffusion-wave equations with initial singularity. First, the original problem is equivalently transformed into its partial integro-differential form. Then, for the time discretization, the Crank-Nicolson technique combined with the midpoint formula and the second order convolution quadrature formula are used. Meanwhile, the classical central difference formula and fractional central difference formula are adopted to approximate the second order derivative and the Riesz derivative in space, respectively. The unconditional stability and convergence of the proposed scheme are proved by the energy method. Numerical experiments support the theoretical results.
- Fractional nonlinear diffusion-wave equations /
- finite difference scheme /
- linearized ADI scheme /
- stability /
- convergence
MSC: 65M06, 65M12

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References

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