Abstract
In this paper, a new method is proposed to solve the time-fractional reaction-diffusion equation with nonlinear variable coefficients. Based on the second-order weighted and shifted Grünwald difference (WSGD) method for time Riemann-Liouville fractional derivative, we formulate and analyze the extrapolated Crank-Nicolson (ECN) method in time and orthogonal spline collocation (OSC) method in space. We prove the optimal global convergence order by a novel choice of the first step solution uh1. Finally, some numerical results are given to verify the convergence rate in the theoretical analysis.
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