A kernel-based technique to solve three-dimensional linear Fredholm integral equations of the second kind over general domains

Abstract

In this article, we study a kernel-based method to solve three-dimensional linear Fredholm integral equations of the second kind over general domains. The radial kernels are utilized as a basis in the discrete collocation method to reduce the solution of linear integral equations to that of a linear system of algebraic equations. Integrals appeared in the scheme are approximately computed by the Gauss–Legendre and Monte Carlo quadrature rules. The method does not require any background mesh or cell structures, so it is mesh free and accordingly independent of the domain geometry. Thus, for the three-dimensional linear Fredholm integral equation, an irregular domain can be considered. The convergence analysis is also given for the method. Finally, numerical examples are presented to show the efficiency and accuracy of the technique.