High Dimensional Model Representation Approximation of an Evolution Operator with a First Order Partial Differential Operator Argument

Abstract

In this work, a novel approximation scheme based on a recently developed representation, called the High Dimensional Model Representation (HDMR), is proposed to approximate evolution operators. The approximation is not developed at the operator level, instead the effect of the operator on an arbitrary function is approximated. The purpose of the work is to investigate how HDMR can be applied for the approximation of evolution operator and its efficiency. Although the approximation can be constructed for any order of multivariance, only the constant and univariate components of HDMR are considered in this work. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)