High Order Numerical Algorithm For Fractional Volterra Integro-differential Equations

Fractional order Volterra integro-differential equation,because its fractional derivative and Volterra integral have nonlocal properties,it can depict the memory and heredity of the material,thus the fractional Volterra integro-differential equation model is widely used in the fields of mathematics,physics,viscoelasticity and subbiology.The first work of this paper is to study the numerical solution of a class of fractional forced vibration equations,the finite difference method is used,the two order derivative and fractional order derivative are approximated,and a high order numerical scheme is constructed to solve the equation,the error analysis and theoretical proof of the format are also given,Finally,some numerical examples are given to illustrate the effectiveness of the proposed scheme.The second main work of this paper is to study the high order numerical algorithm of fractional Volterra Integro-differential equation and draw on the modified block-by-block method for solving the fractional ordinary differential equation,the fractional Volterra integral equation is converted to the equivalent Volterra integral equation,and the integral form of the equation is based on the modified block-by-block thought.The high order numerical scheme for solving the equation is obtained,the error analysis and relevant theoretical proof of the format are carried out.Finally,a numerical example is given to demonstrate the rationality of the scheme.