Abstract
•We introduce Legendre-Chebyshev spectral collocation method.•A high accurate spectral algorithm for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional (RF-TNRDEs) is consider.•This work is the extension of our studies on the spectral collocation methods.
A high accurate spectral algorithm for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional (RF-TNRDEs) is consider. We propose a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the RF-TNRDEs. A complete theoretical formulation is presented and numerical examples are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle RF-TNRDEs is revealed.