A linearized finite difference/spectral-Galerkin scheme for three-dimensional distributed-order time-space fractional nonlinear reaction-diffusion-wave equation: Numerical simulations of Gordon-type s

Release Time:2025-04-30  Hits:

• Date:2025-04-30
• Title of Paper:A linearized finite difference/spectral-Galerkin scheme for three-dimensional distributed-order time-space fractional nonlinear reaction-diffusion-wave equation: Numerical simulations of Gordon-type s
• Journal:Computer Physics Communications
• Summary:In this paper, we construct a novel linearized finite difference/spectral-Galerkin scheme for three-dimensional distributed
  -order time-space fractional nonlinear reaction-diffusion-wave equation. By using Gauss-Legendre quadrature
  rule to discretize the distributed integral terms in both the spatial and temporal directions, we first approximate the
  original distributed-order fractional problem by the multi-term time-space fractional differential equation. Then, we
  employ the finite difference method for the discretization of the multi-term Caputo fractional derivatives and apply the
  Legendre-Galerkin spectral method for the spatial approximation. The main advantage of the proposed scheme is that
  the implementation of the iterative method is avoided for the nonlinear term in the fractional problem. Additionally,
  numerical experiments are conducted to validate the accuracy and stability of the scheme. Our approach is showcased
  by solving several three-dimensional Gordon-type models of practical interest, including the fractional versions
  of sine-, sinh-, and Klein-Gordon equations, together with the numerical simulations of the collisions of the Gordontype
  solitons. The simulation results can provide a deeper understanding of the complicated nonlinear behaviors of
  the 3D Gordon-type solitons.
• Co-author:S. Guo, L. Mei, Z. Zhang, C. Li, M. Li, Y. Wang
• Volume:252(107144)
• Translation or Not:No
• Date of Publication:2020-04-30