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An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations

机译：一维时间分数阶Burgers方程的隐式差分格式和算法实现

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摘要

An implicit difference scheme with the truncation of order 2 - alpha(0 < alpha < 1) for time and order 2 for space is considered for the one-dimensional time-fractional Burgers equations. The L-1-discretization formula of the fractional derivative in the Caputo sense is employed. The second-order spatial derivative is approximated by means of the three-point centered formula and the nonlinear convection term is discretized by the Galerkin method based on piecewise linear test functions. The stability and convergence in the L-infinity norm are proved by the energy method. Meanwhile, a novel iterative algorithm is proposed and implemented to solve the nonlinear systems. Numerical experiment shows that the results are consistent with our theoretical analysis, and the comparison between the proposed iterative algorithm and the existing methods shows the efficiency of our method. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
机译：对于一维时间分数阶Burgers方程，考虑了一种隐式差分方案，该方案的截断时间为2-alpha（0

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