ASYMPTOTIC EXPANSIONS OF APPROXIMATE SOLUTIONS OF INTEGRAL EQUATIONS AND EIGENVALUE PROBLEMS IN A MODIFIED VERSION OF THE ITERATED COLLOCATION METHOD WITH GREEN’S TYPE KERNEL

Abstract

In the literature, asymptotic expansions for certain approximate solutions of operator equations and eigenvalues associated with Green’s kernel are not justified in the case of iterated collocation method for piecewise polynomial space of degree $\ge 2$. In this paper, we prove the existence of asymptotic expansion of operator equations at partition points and for a simple eigenvalue associated with Green’s type kernel. A numerical example is considered to illustrate theoretical results.