Numerical solution of high-order Volterra-Fredholm integro-differential equations by using Legendre collocation method

The main purpose of this paper is to use the Legendre collocation spectral method for solving the high-order linear Volterra-Fredholm integro-differential equations under the mixed conditions. Avoiding integration of both sides of the equation, we expressed mixed conditions as equivalent integral equations, by adding the neutral term to the equation. Error analysis for approximate solution and approximate derivatives up to order k of the solution is obtained in both L2 norm and L∞ norm. To illustrate the accuracy of the spectral method, some numerical examples are presented.