A kind of generalized backward differentiation formulae for solving fractional differential equations

作者：

Highlights：

• A new kind of numerical method is established based on generalized backward differentiation formulae for solving fractional ordinary differential equation.

• This method has good stability and can avoid the order barrier of the numerical methods which are based on convolution quadrature.

• The convergence and stability of this method are analyzed by using an estimation of the inverse of Toeplitz matrix.

摘要

•A new kind of numerical method is established based on generalized backward differentiation formulae for solving fractional ordinary differential equation.•This method has good stability and can avoid the order barrier of the numerical methods which are based on convolution quadrature.•The convergence and stability of this method are analyzed by using an estimation of the inverse of Toeplitz matrix.

论文关键词：Fractional ordinary differential equation,Generalized backward differentiation formulae,Convergence,Stability

论文评审过程：Received 5 November 2019, Revised 12 October 2021, Accepted 12 December 2021, Available online 27 December 2021, Version of Record 27 December 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126872