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A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity

  • Emadidin Gahalla Mohmed Elmahdi and Jianfei Huang EMAIL logo
Published/Copyright: October 6, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 5

Abstract

This paper presents a linearized finite difference scheme for solving a kind of time-space fractional nonlinear diffusion-wave equations with initial singularity, where the Caputo fractional derivative in time and the Riesz fractional derivative in space are involved. First, the considered problem is equivalently transformed into its partial integro-differential form. Then, the fully discrete scheme is constructed by using the Crank–Nicolson technique, the L1 approximation, and the convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and the fractional central difference formula are applied to approximate the second-order derivative and the Riesz fractional derivative in space, respectively. Moreover, the stability and convergence of the proposed scheme are strictly proved by using the discrete energy method. Finally, some numerical experiments are presented to illustrate the theoretical results.

Keywords: convergence; fractional nonlinear diffusion-wave equations; initial singularity; linearized scheme; stability
Mathematics Subject Classification: 65M06; 65M12
Corresponding author: Jianfei Huang, College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China, E-mail:

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11701502

Award Identifier / Grant number: 11871065

Funding source: Natural Science Foundation of Jiangsu Province of China

Award Identifier / Grant number: BK20201427

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This research is supported by Natural Science Foundation of Jiangsu Province of China (Grant No. BK20201427), and by National Natural Science Foundation of China (Grant Nos. 11701502 and 11871065).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-10-12
Revised: 2022-09-05
Accepted: 2022-09-18
Published Online: 2022-10-06

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0388
Keywords for this article
convergence; fractional nonlinear diffusion-wave equations; initial singularity; linearized scheme; stability

Articles in the same Issue

  1. Frontmatter
  2. Original Research Article
  3. Hybrid solitary wave solutions of the Camassa–Holm equation
  4. Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
  5. A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
  6. Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
  7. Numerical modeling of the dam-break flood over natural rivers on movable beds
  8. A class of piecewise fractional functional differential equations with impulsive
  9. Lie symmetry analysis for two-phase flow with mass transfer
  10. Asymptotic behavior for stochastic plate equations with memory in unbounded domains
  11. Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
  12. A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
  13. Ground state solutions of Schrödinger system with fractional p-Laplacian
  14. Bifurcation analysis of a new stochastic traffic flow model
  15. An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
  16. Hilfer fractional stochastic evolution equations on infinite interval
  17. Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
  18. Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
  19. Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
  20. Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
  21. Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
  22. Shehu transform on time-fractional Schrödinger equations – an analytical approach
  23. A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
  24. Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
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