On numerical treatments to solve nonlinear mixed integral equation

DOI: 10.5176/2251-1911_CMCGS16.12

Authors: Sameeha Ali Raad

Abstract: In this paper, a nonlinear mixed integral equation (NMIE) with continuous kernels in the space , - , - under certain conditions is considered. The existence of a unique solution, using Banach Fixed Point theorem, is considered. Then, a quadratic numerical method is used to obtain a system of Fredholm integral equations (NSFIEs), we assume a quadratic method and Simpson rule to obtain, in each method, a nonlinear algebraic system (NAS). The existence of a unique solution of each nonlinear system, is considered. Numerical results are calculated and the error estimate, in each case, is computed.

Keywords: Mixed integral equation (MIE); Nonlinear system of Fredholm integral equations (NSFIEs); Quadratic method (QM); Simpsosn's rule ( SR ); Nonlinear algebraic system (NAS).