A collocation method for solving some integral equations in distributions

TL;DR

This paper introduces a collocation method for numerically solving integral equations with kernels involving positive rational functions of elliptic operators, demonstrating its efficiency and stability through numerical examples.

Contribution

The paper develops a novel collocation approach tailored for integral equations with complex elliptic operator kernels, expanding computational techniques in this area.

Findings

Method shows high efficiency in numerical experiments.

Approach is stable across various test cases.

Effective for integral equations with elliptic operator kernels.

Abstract

A collocation method is presented for numerical solution of a typical integral equation Rh :=\int_D R(x, y)h(y)dy = f(x), x {\epsilon} D of the class R, whose kernels are of positive rational functions of arbitrary selfadjoint elliptic operators defined in the whole space R^r, and D \subset R^r is a bounded domain. Several numerical examples are given to demonstrate the efficiency and stability of the proposed method.