Analyzing the NystromMethod for Second Kind Fredholm Integral Equations

Abstract

This research proposal aims to study if second-kind Fredholm Integral Equations can possibly be solved using the Nystrom Method, which are common in many different fields and which require for the development of effective numerical solutions. The Nystrom Method will be thoroughly examined, along with an explanation of how it applies to second-kind Fredholm Integral Equations. Additionally, it will look at how different parameters influence the convergence of the Nystrom Method, such as the number of discretization points and the choice of numerical quadrature. The expected outcomes are meant to deepen our understanding and facilitate the advancement of numerical algorithms, leading to a more reliable and efficient solutions for integral equations. This discovery holds importance for numerous scientific and engineering domains, and it can lead in advancements in computer methodologies.