Study on Some Particular Class of Nonlinear Integral Equation with a Hybridized Approach

This article deals with a particular class of integral equations involving pure delay term. The existence of a solution is described using fixed point theory. Moreover, a hybridized scheme is proposed to investigate the approximate solution. In this context, boundary element method is used with piecewise linear interpolation. Also, an algorithm is there for error estimation and in support of the considered numerical method stability analysis is done. This testimony completely demonstrates the comprehensive study of the considered class of integral equation and understanding the behaviour of the approximate solution in the presence of delay.