A higher-order finite difference method for solving a system of integro-differential equations

A finite difference method and Gauss method of numerical integration are used to approximate the integro-differential system of Eq. (1) with the global error z(h)=O(h4). The resulting system of algebraic equations is solved by efficient implicit iterations. A Mathematica module is designed for the purpose of testing and using the method. An example of an integral–differential equation with the Greenʹs function as the kernel is solved.