Abstract.

In this article, a fast numerical scheme is investigated to approximate nonlinear mixed Volterra-Fredholm integral equations based on expansion method. In the approximation procedure, we use expansion method in order to transform these two-dimensional integral equations into a differential equation. After making boundary conditions, this differential equation decreases to a system algebraic equations that can be solved simply using any of the common methods. The main characteristic of this scheme is low computational cost and CPU time to achieve an appropriate solution. Error analysis and comparisons with other existing schemes demonstrate the efficiency of the proposed scheme

Keywords:

two-dimensional expansion, linear and nonlinear systems, mixed Volterra-Fredholm integral equations, boundary conditions