Abstract: Aiming at the problem of the numerical solution of higher order convolution integro-differential equation. Firstly, the discrete numerical scheme of higher order convolution integro-differential equation was constructed by using barycentric rational interpolation collocation method, and the global convergence theorem was given. Secondly, by selecting equidistant nodes and corresponding configuration parameters, the effectiveness of the method was verified by numerical examples.

Key words: higher order convolution integro-differential equation, barycentric rational interpolation, collocation method