Acceleration of convergence in approximate solutions of Urysohn integral equations with Green's kernels

Abstract

Consider a non-linear operator equation $x-K(x)=f$, where $f$ is a given function and $K$ is a Urysohn integral operator with Green's function type kernel defined on $L^{\infty }[0,1]$. We apply approximation methods based on interpolatory projections onto the approximating space ${\mathcal{X}}_n$, which is the space of piecewise polynomials of even degree with respect to a uniform partition of $[0,1]$. The approximate solutions obtained from these methods demonstrate enhanced accuracy compared to the classical collocation solution for the same equation. Numerical examples are given to support our theoretical results.

References in corpus (1)

• A note on improvement by iteration for the approximate solutions of second kind Fredholm integral equations with Green's kernels