On Nonlinear Integral Operator of Trigonometric Type Using Modified Newton Method

Abstract

The Modified Newton method (MNM) is applied to obtain the approximate solution to the system of nonlinear Volterra type integral equation with the trigonometric kernel function. Modified Newton method (MNM) is used to linearized the system then solved by the Nystrom type Gauss-Legendre quadrature formula (QF). A new majorant function is stated which leads to the increment of convergence interval. The existence and uniqueness of approximate solution are proved. Sufficient condition for the approximate solution is established and their validity is illustrated with example.