Collocation Method for Functional 3-Kind Volterra Integral Equations

Abstract

In this work, we present a numerical approach based on the collocation method for solving weakly singular Volterra Integral Equations of the Third Kind (3K-VIEs) with proportional delays. We employ modified graded meshes to analyze the solvability and convergence of the proposed method. Furthermore, we rigorously establish the convergence rate in terms of the parameter p for the collocation scheme using m collocation parameters. To validate the theoretical findings, we provide numerical examples, demonstrating the reliability and effectiveness of the method.