On high order numerical schemes for fractional differential equations by block-by-block approach

作者：

Highlights：

• An improved numerical scheme are proposed to solve the nonlinear fractional differential equations with non-smooth solution.

• The change of variable and the block-by-block method are introduced to propose a novel high-order scheme, and the method can reduce the computational cost.

• The advantage of the improved block-by-block method is that the solution completely decoupled at each block step expect for the first two steps. We can compute the equation directly.

• The convergence of the proposed scheme is proved.

摘要

•An improved numerical scheme are proposed to solve the nonlinear fractional differential equations with non-smooth solution.•The change of variable and the block-by-block method are introduced to propose a novel high-order scheme, and the method can reduce the computational cost.•The advantage of the improved block-by-block method is that the solution completely decoupled at each block step expect for the first two steps. We can compute the equation directly.•The convergence of the proposed scheme is proved.

论文关键词：Nonlinear fractional differential equation,High order scheme,Convergence,Non-smooth solution

论文评审过程：Received 20 December 2021, Revised 13 March 2022, Accepted 15 March 2022, Available online 26 March 2022, Version of Record 26 March 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127098