Indian Journal of Industrial and Applied Mathematics
  • Year: 2014
  • Volume: 5
  • Issue: 2

Numerical Solutions of Non-linear Fredholm Integro-Differential Equations of Second Kind

1Research Scholar, Department of Mathematics, Shivaji University, Kolhapur-416004, Maharashtra, India

2Professor, Department of Mathematics, Shivaji University, Kolhapur-416004, Maharashtra, India

*(*Corresponding Author) E-mail Id: *asmashaikh30l@gmail.com;

**saritakolhapur@gmail.com

Abstract

In this paper, we propose a method that determines the approximate solution of nonlinear Fredholm integro-differential equations of second kind. The integro-differential equation is converted into an integral equation by using suitable transformation. The integral part is approximate by Newton Cote's method. The convergence of method is established. The theory is supported by some examples.

Keywords

Fredholm integro-differential equation, Lipschitz type kernel function, Newton Cote‘s method, Trapezoidal rule, Simpson‘s rule, Convergence, Iterative method