Richardson extrapolation of Kantorovich and degenerate kernel methods for Fredholm integral equations of the second kind

Document Type : Original Article


University Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, Morocco



In this paper, we propose two methods based on projections for approximating the solution of Fredholm integral equations of the second kind. The projection is either the orthogonal projection or an interpolatory projection onto a space of piecewise polynomials of any degree $\leq r-1$. We show that the two methods have asymptotic series expansions and the orders of convergence can be further improved by multi-step Richardson extrapolation, where the calculation are repeated with each subinterval halved. These orders of convergence are preserved in the corresponding discrete methods obtained by calculating the integrals with a numerical quadrature formula. Numerical examples are given to validate the theoretical estimates.