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 Grunwald 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 u h 1 . Finally, some numerical results are given to verify the convergence rate in the theoretical analysis.

中文翻译：

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非线性时间分数阶反应扩散方程的外推 CN-WSGD OSC 方法

摘要 本文提出了一种求解具有非线性变系数的时间分数阶反应扩散方程的新方法。基于时间Riemann-Liouville分数阶导数的二阶加权和移位Grunwald差分（WSGD）方法，我们制定并分析了时间上的外推Crank-Nicolson（ECN）方法和空间上的正交样条搭配（OSC）方法。我们通过第一步解决方案 uh 1 的新选择来证明最优全局收敛阶。最后，给出了一些数值结果来验证理论分析中的收敛速度。