Numerical Solution of 2D Nonlinear Volterra-Fredholm Integral Equations using Polynomial Collocation Method

Abstract

In this research, polynomial collocation method was used to develop and implement numerical solutions of nonlinear two-dimensional (2D) mixed Volterra-Fredholm integral equations. The Integral equation was transform into systems of algebraic equations using standard collocation points with Bernstein polynomial as a basis function and then solves the nonlinear algebraic equations using Newton-Rhapson method. The analysis of the developed method was investigated and the solution was found to be unique and convergent. To illustrate the efficiency, simplicity, and accuracy of the approach, illustrative examples are provided which shows that the method outperforms the other methods