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

Abstract

This paper is concerned with numerical solutions for a class of nonlinear stiff fractional differential equations (SFDEs). By combining the underlying one-leg methods with piecewise linear interpolation, a type of extended one-leg methods for nonlinear SFDEs with γ-order (0 < γ < 1) Caputo derivatives are constructed. It is proved under some suitable conditions that the extended one-leg methods are stable and convergent of order min{p,2−γ}, where p is the consistency order of the underlying one-leg methods. Several numerical examples are given to illustrate the computational efficiency and accuracy of the methods.