A Study of Error Estimation for Second Order Fredholm Integro-Differential Equations

In this work, we study efficient asymptotically correct a posteriori error estimates for the numerical approximation of second order Fredholm integro-differential equations. We use the defect correction principle to find the deviation of the error estimation and show that collocation method by using m degree piecewise polynomial provides order O ( h m + 2 ) for the deviation of the error. Also, the theoretical behavior is tested on examples and it is shown that the numerical results confirm theoretical analysis.