Runge-Kutta Convolution Quadrature Methods For Two Kinds Of Fractional Differential Equations

During the past several decades,fractional differential equations have widely applied in science fields such as physics,neuron modeling,materials science,and biology.With the emergence of fractional differential equations in more and more scientific fields,it is very urgent to study the theoretical analysis and numerical calculation of fractional differential equations.Therefore,we use to Runge-Kutta convolution quadrature(RKCQ)method to solve a class of nonlinear fractional differential equations with delay and time-fractional sub-diffusion equations.The main contents of this paper are as follows:1.We introduce the definition form of fractional derivative and some basic knowl-edge of RKCQ methods.Meanwhile,the numerical scheme for solving nonlinear fractional differential equations by RKCQ methods are reviewed.2.A class of difference methods for solving nonlinear fractional differential equations with delay is constructed.Convergence and stability analysis of these methods are proved.Numerical experiments are performed to show their effectiveness and some related theoretical results.3.By combined the RKCQ methods with the spatial second-order central difference method and the spatial fourth-order compact difference method,a class of difference methods for solving time-fractional sub-diffusion equations is constructed,and the convergence and stability of these methods are proved.Finally,some numerical experiments are provided to show their effectiveness and some related theoretical results.