SEMI-ANALYTICAL AND NUMERICAL SOLUTION FOR GENERALIZED NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS

Abstract

We study two semi-analytical methods: the successive approximation method, that is, the Picard method (PM), the Adomian decomposition method (ADM), and one numerical technique (NT) method for finding the approximate solution of generalized nonlinear functional integral equations (GNFIE). The existence and uniqueness results are proved by applying Banach’s contraction theorem. In some cases, it is difficult to find the integral when we use the ADM to find the approximate solution of certain nonlinear integral equations. To overcome this problem, some numerical techniques are applied based on GNFIE. Our existence results contain many functional integral equations as a special case. Finally, we discuss some examples and compare the methods along with the error analysis.