Convergence Analysis of Sinc-Collocation Scheme With Composite Trigonometric Function for Fredholm Integral Equations of the Second Kind

Abstract

The paper discusses the convergence of Sinc collocation scheme for the solution of Fredholm integral equation of the second kind. A modified composite trigonometric function is employed as a variable transformation function for this procedure. We first show that the constructed variable transformation function decays exponentially and thus satisfies the conditions for the error bound associated with single exponential transformation functions. Next, the convergence analysis of the scheme showing exponential convergence is discussed. Finally, some numerical examples are presented to illustrate the efficiency and stability of the numerical scheme.