A high-order numerical scheme for solving nonlinear time fractional reaction-diffusion equations with initial singularity

摘要

We propose a high-order numerical scheme for nonlinear time fractional reaction-diffusion equations with initial singularity, where L2-1_σ scheme on graded mesh is used to approximate Caputo fractional derivative and Legendre spectral method is applied to discrete spatial variable. We give the priori estimate, existence and uniqueness of numerical solution. Then the unconditional stability and convergence are proved. The rate of convergence is O(M~(-min{rα，2}) + N~(-m)), which is obtained without extra regularity assumption on the exact solution. Numerical results are given to confirm the sharpness of error analysis.