Numerical solutions to one dimensional linear Volterra–Fredholm integral equations based on LS-SVM model

Abstract

This paper introduces a novel numerical approach using least squares support vector machine (LS-SVM) to handle one dimensional linear Volterra–Fredholm integral equations. This method can also handle weak singular kernel Fredholm/Volterra integral equations and linear systems of Volterra–Fredholm integral equations. By minimizing errors and utilizing least squares support vector machines, the approach derives continuous closed-form solutions to the origin problem. Ultimately, the method offers an efficient numerical approximation for solving Volterra–Fredholm integral equations through the resolution of linear equations. The paper includes multiple numerical examples that demonstrate the effectiveness and superiority of the proposed method.