One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives

作者：

Highlights：

• A type of extended one-leg methods are constructed for a class of nonlinear stiff fractional differential equations.

• Under some suitable conditions, the extended one-leg methods are proved to be stable and convergent of order min{p,2−γ}.

• Several interesting numerical examples are presented to illustrate the computational efficiency and accuracy of the extended one-leg methods.

摘要

•A type of extended one-leg methods are constructed for a class of nonlinear stiff fractional differential equations.•Under some suitable conditions, the extended one-leg methods are proved to be stable and convergent of order min{p,2−γ}.•Several interesting numerical examples are presented to illustrate the computational efficiency and accuracy of the extended one-leg methods.

论文关键词：Nonlinear stiff fractional differential equations,Caputo derivatives,Extended one-leg methods,Convergence,Stability,Numerical experiment

论文评审过程：Received 6 May 2018, Revised 27 October 2018, Accepted 11 December 2018, Available online 26 December 2018, Version of Record 26 December 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.12.019