An Efficient Spectral Galerkin Method for Two‐Dimensional Fredholm Integral Equations in Complex Domains

ABSTRACT Fredholm integral equations are an important class of integral equations widely used in science and engineering. This paper aims to numerically solve Fredholm integral equations of the second kind in two‐dimensional complex domains using a combination of spectral methods and mapping techniques. First, we map the computational domain onto a rectangular domain through coordinate transformation. Then, within this rectangular domain, we employ the classical spectral method for numerical simulation. Our analysis focuses on discussing the existence, uniqueness, and convergence of numerical solutions. Numerical results demonstrate that the proposed method achieves high‐order accuracy.