L2 error estimate of a nonuniform H2N2 difference scheme for the 2D nonlinear time‐fractional reaction‐diffusion‐wave equation
Zhihao Sheng, Yang Liu, Yonghai Li
Source abstract
Abstract In this article, we develop a numerical method to solve the 2D nonlinear time‐fractional reaction‐diffusion‐wave equation using the finite difference method combined with the formula on nonuniform time meshes. To improve the computational efficiency, we use a linearized approximation of nonlinear term. We specifically derive a discrete fractional inequality based on the formula to analyze the numerical methods on nonuniform time meshes for time‐fractional wave equations. With the help of this inequality, we derive the stability and the error estimate of our numerical method. We present numerical experiments to confirm the feasibility and effectiveness.
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