A spline collocation method for Fredholm–Hammerstein integral equations of the second kind in two variables

摘要

We consider Fredholm–Hammerstein integral equations of the second kind over a rectangular region in plane. As in Kumar and Sloan (1987) [5], we reformulate it into an equivalent integral equation. For the alternative equation, we triangulate the rectangular domain and on each triangle use a collocation method based on constant spline approximation. We discuss the convergence of the approximate solutions and conclude the paper with numerical examples.