Linear Fredholm Integro-Differential Equation of the Second Kind

In this thesis we focus on solving linear Fredholm integro-differential equation of the second kind due to it's wide range of physical applica- tions. We will investigate some analytical and numerical methods to solve this equation. The discussed analytical methods include: Direct computation method, variational iteration method, Adomian decompos- ition method, modified decomposition method, noise terms phenomenon and series solution method. The numerical methods that will be presented here are: B-spline scaling function and wavelet method, Homotopy perturbation method, Legendre polynomial method and Taylor collocation method. Particular numerical examples demonstrating these numerical methods have been implement- ed for solving linear Fredholm integro-differential of the second kind. A comparison has been drawn between these numerical methods. Our numerical results show that the Homotopy perturbation method and Legendre polynomial method have proved to be the most efficient in comparison to the other numerical methods regarding their performance on the used examples.