A COMPARATIVE SOLUTION ON NONLINEAR FREDHOLM INTEGRAL EQUATION OF SECOND KIND

ABSTRACT This project research present the study of nonlinear Fredholm integral equation of the second kind by comparing the method of classical Adomian and modified Adomian decomposition methods with exact solution.The numerical method considered were used to solve the nonlinear Fredholm integral equation using some numerical examples in order to determinethe efficiency of each methods when are compared with exact solution. The results obtained shows a slight error differenceswhich illustrated the reliability and the performance of the methods used. The result for rate of convergence between Adomian decomposition method (ADM) and Modified decomposition method (MADM) with exact solutions was obtained and presented are found to converge very quickly and are more accurate. The absolute error between the classical Adomian and modified Adomian decomposition method with the exact solution was also observed with relatively insignificant differences which shows a good agreement between the methods with the exact solution. The Adomian polynomial were also used which represent the nonlinear term in the classical Adomian decomposition and modified Adomian decomposition methods of solving Nonlinear Fredholm integral equation of the second kind , and the simple and practical scheme that will construct Adomian polynomial begins by assuming that the nonlinear term u^n (x)under the integral sign of the Fredholm integral equation is equated to the polynomial series. The results of two numerical methods together with that of Exact solution are presented both in line graph and table for comparison. MATLAB software was also employed for numerical solution and line graph.