A general convergence theory for nonlinear equations with application to integro-differential equations

Abstract

This paper is concerned with approximate solutions of an abstract and a concrete nonlinear equation. The abstract operator equation is motivated by numerical approximation of a nonlinear integro-differential equation (IDE) which exhibits certain features arising in the modelling of catallytic combustion in a cylindrical reactor taking into account of radiation. We give a general convergence result for approximate solutions of nonlinear operator equations using prolongation and restriction operators. This answers an open question on the stability of certain nonlinear operators. We apply the general convergence theory to the nonlinear IDE.