LAUSR

A finite difference/pseudospectral scheme is developed for solving nonlinear time fractional parabolic equations with Caputo fractional derivative of order . The boundedness and unique solvability of numerical solution are given. Then we prove rigorously the unconditional stability and convergence of the fully discrete scheme, where the optimal error estimate in norm is obtained. Furthermore, an improved scheme by adding correction terms is proposed to deal with the weak singularity, which makes the approximations of fractional derivative and nonlinear term exact or sufficiently accurate for the weak singular parts of solutions. Numerical experiments are provided to show the sharpness of the error analysis.