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A time two-grid algorithm for the two dimensional nonlinear fractional PIDE with a weakly singular kernel

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  • Wang, Furong
  • Yang, Xuehua
  • Zhang, Haixiang
  • Wu, Lijiao

Abstract

The main aim of this paper is to solve the two-dimensional nonlinear fractional partial integro-differential equation (PIDE) with a weakly singular kernel by using the time two-grid finite difference (FD) algorithm. The second-order backward difference formula (BDF) and L1 scheme are used in time. The time two-grid algorithm is constructed to improve the solving efficiency of nonlinear systems. The Newton iteration is used to solve nonlinear discrete system on the coarse grid, and then we apply Lagrangian linear interpolation to attain the function value used in constructing the difference scheme on the fine grid. The second-order finite difference method (FDM) is used in space. The unconditional stability and convergence are attained for the two-grid fully discrete system. Numerical experiments show that the used CPU time for the presented two-grid numerical algorithm is lower than the general finite difference method for solving the nonlinear system.

Suggested Citation

  • Wang, Furong & Yang, Xuehua & Zhang, Haixiang & Wu, Lijiao, 2022. "A time two-grid algorithm for the two dimensional nonlinear fractional PIDE with a weakly singular kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 38-59.
    • Handle: RePEc:eee:matcom:v:199:y:2022:i:c:p:38-59
    DOI: 10.1016/j.matcom.2022.03.004
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    References listed on IDEAS

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    1. Zhao, Yong-Liang & Zhu, Pei-Yong & Luo, Wei-Hua, 2018. "A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 231-248.
    2. Qiu, Wenlin & Chen, Hongbin & Zheng, Xuan, 2019. "An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 298-314.
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