Convergence and stability of block boundary value methods applied to nonlinear fractional differential equations with Caputo derivatives

摘要

In this paper, by combining the p-order block boundary value methods with the m-th Lagrange interpolation, a class of new numerical methods for solving nonlinear fractional differential equations with the gamma-order (0 gamma 1) Caputo derivatives are obtained. It is proved under some appropriate conditions that the induced methods are convergent of order min {p, m - gamma + 1 } and globally stable. Several numerical examples are given to illustrate the theoretical results and the computational effectiveness and accuracy of the methods. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.