The backward substitution method for multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type

The paper presents a new numerical method for solving multipoint boundary value problems for Volterra–Fredholm integro-differential equations with linear functional arguments. The method consists of replacing the initial equation by an approximate equation which has an exact analytic solution with a set of free parameters. These free parameters are determined by the use of the collocation procedure. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results. Numerical results show that the proposed method is of high accuracy and is efficient for solving a wide class of the functional integro-differential equations of the most general form.