A Bernstein operational matrix approach for solving a system of high order linear Volterra–Fredholm integro-differential equations

In this paper, we present some efficient direct solvers for solving a system of high order linear Volterra–Fredholm integro-differential equations (VFIDEs). A new approach implementing a collocation method in combination with operational matrices of Bernstein polynomials for the numerical solution of VFIDEs is introduced. The main characteristic behind this approach is that it reduces such problems to ones of solving systems of algebraic equations. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving systems of high order linear VFIDEs.