The order completion method for nonlinear partial differential equations

Abstract

In this paper we focus on the fundamentals of the Order Completion Method (OCM) for differential algebras of generalized functions. This OCM is used for various systems of nonlinear partial differential equations. Generally, outcome for generalized results of initial value problems achieved with the help of OCM. The results we find fulfill the initial condition in appropriate manner, and all the outcomes can be demonstrated in a canonical way with the use of generalized partial derivatives. The solution is based on characterization of order convergence of various sequences of quasi-continuous functions in a manner of piecewise convergence of this type of sequences. Moreover the differential algebras are corresponding to the dense algebras illustrated by Rosinger & Verneave.