Runge-Kutta Methods For Fractional Differential Equation

With the rapid development of high technology,fractional differential equations had been widely used in materials science,computational biology and other fields.In this paper,the model considered is derived from material science,and the numerical methods for fractional differential equation of this model in literature have been studied at home and abroad,such as high order fractional BDF method.But it have not been studied by Runge-Kutta method.This paper constructed the high order format of non-linear fractional differential equation that solved by fractional Radauâ…¡A method and fractional general Runge-Kutta method firstly.We proved the compatibility and convergence of the two methods, and gave out the stability analysis of Radauâ…¡A method.The numerical example compared the approximation with the same order of BDF method at last,and showed that Runge-Kutta method is a more effective method than BDF to solve the fractional differential equation.