Several Kinds Of Runge-kutta Methods For Fractional Differential Equations

Based on a high order approximation of L-stable Runge-Kutta methods for Riemann-Liouville fractional dirivatives,a class of high-order L-stable Runge-Kutta methods for solving the nonlinear fractional differential equations is con-structed in this paper.Consistency, convergence, and stability analysis of these methods are given. In numerical experiments,fractional Radau IA methods and Lobattoâ…¢C methods and singly-diagonal implicit Runge-Kutta methods com-bining the short memory principle are chosen.These methods are efficient for solving nonlinear fractional differential equations.