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

A new kind of numerical method based on generalized backward differentiation formulae is established for solving fractional differential equations. An estimate of the inverse of a class of Toeplitz matrix, which is related to the method, is given. By using the estimate, convergence and stability of the method are analyzed. It is shown that the method has high order of convergence and good stability. Some numerical experiments are also given to illustrate the effectiveness of the method. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

A new numerical method based on generalized backward differentiation formulae is proposed for solving fractional differential equations. The method demonstrates high order of convergence and good stability, which is supported by numerical experiments.