Orthogonal collocation for a nonlinear integro-differential equation

This paper is concerned with the numerical solution using orthogonal collocation of a nonlinear integro-differential equation which exhibits certain features arising in the modelling of catalytic combustion in a cylindrical reactor taking account of radiation. These features imply that the available convergence theory of orthogonal collocation cannot be applied directly. Optimal convergence results of the orthogonal collocation approximation are proved for our equation, and these are illustrated by numerical experiments. In addition superconvergence results for the iterated collocation solution are obtained.