APPROXIMATE SOLUTIONS for SYSTEM of NONLINEAR VOLTERRA INTEGRAL EQUATION of the FIRST KIND VIA OHAM and MOHAM

This paper is aimed to find an approximate solution to system of nonlinear Volterra integral equations of the first kind (SNVIEFK), by applying optimal homotopy asymptotic method (OHAM) which is powerful and efficient method and a new approach called Multistage optimal homotopy asymptotic method (MOHAM). MOHAM is just clear alteration of the standard OHAM, in which in order to find a more accurate approximate solution, OHAM will be applied in a consecutive sequence of subintervals.The results confirm efficiency and ability of these methods for such equation of the SNVIEFK. The numerical results will be compared, to find out that which method of these two is more accurate. Advantages of applying MOHAM are also illustrate.

Keywords:

Optimal homotopy asymptotic method (OHAM) , Multistage optimal homotopy asymptotic method MOHAM) , weakly singular Fredholm integral equations of the second kind , Series solutions