Approximate Solution of System of Nonlinear Volterra Integro-Differential Equations by Using Bernstein Collocation Method

Abstract. This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro- differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points, this approach reduces the systems of Volterra integro- differential equations associated with the given conditions, to a system of nonlinear algebraic equations. By solving such arising nonlinear system, the Bernstein coefficients can be de- termined to obtain the nite Bernstein series approach. Numerical examples are tested and the resultes are incorporated to demonstrate the validity and applicability of the approach. Comparisons with a number of conventional methods are made in order to verify the nature of accuracy and the applicability of the proposed approach.