Asymptotic Expansions for Approximate Solutions of Hammerstein Integral Equations with Green's Function Type Kernels

Abstract

We consider approximation of a nonlinear Hammerstein equation with a kernel of the type of Green's function using the Nyström method based on the composite midpoint and the composite modified Simpson rules associated with a uniform partition. We obtain asymptotic expansions for the approximate solution un at the node points as well as at the partition points and use Richardson extrapolation to obtain approximate solutions with higher orders of convergence. Numerical results are presented which confirm the theoretical orders of convergence.

Keywords:

• Hammerstein equation
• Green's function type kernels
• Nyström method
• asymptotic expansion

AMS Subject Classification:

• 45B05
• 65R20