An efficient Galerkin spectral method for two-dimensional fractional nonlinear reaction-diffusion-wave equation
The authors analyze a numerical scheme approximating a two-dimensional fractional nonlinear reaction-diffusion-wave equation. The model considered includes for instance time-fractional Klein-Gordon and sine-Gordon equations. The space discretization is performed using the Legendre-Galerkin spectral methods whereas an alternating direction implicit (ADI) method based on the Crank-Nicolson scheme is used in time. Stability and convergence of the proposed scheme are provided. Some numerical examples are presented.
nonlinear fractional differential equation
scientific article; zbMATH DE number 6929642
scientific article