Numerical Solution of Two Dimensional Mixed Volterra-Fredholm Integral Equations Using Polynomial Collocation Method

In this research, polynomial collocation method was used to develop and implement the numerical solution of linear two-dimensional mixed Volterra-Fredholm integral equations (L2D MVFIE). The Integral equation was transform into systems of algebraic equations using standard collocation points with Bernstein polynomial as a basis function and then solved the linear algebraic equations using Gaussian elimination method. To illustrate the effectiveness, accuracy and efficiency of the approach, illustrative examples are provided. It demonstrates that the method converge faster to the exact solution as the value of N increases.