Computational Method based on Operational Matrices for Special Kind of Volterra Integro-Differential Equation

In this paper, we presented the application of operational matrix in solving special kind of Volterra integro-differential equation. The operational matrix method converts Volterra integro-differential equations into the system of algebraic equations, which is a considerable complexity reduction. Since the operational matrix contains many zero entries, it shows lower computational complexity with respect to the other approximations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive. A good agreement between the obtained solution and a well-known result has been obtained. The test function is provided to show high accuracy and efficiency of the proposed method. This method is capable of greatly reducing the size of calculations while still maintaining high accuracy of the numerical solution.