Residual models for nonlinear partial differential equations

Date

2005-11-30

Authors

Pantelis, Garry

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate method is presented for computing the residuals. These residual models are independent of free or artificial parameters and there direct link with the functional form of the system of PDEs which describe the fully resolved system are established.

Description

Keywords

Partial differential equations, Nonlinear evolution, Contact manifolds, Mathematical modelling

Citation

Pantelis, G. (2005). Residual models for nonlinear partial differential equations. Electronic Journal of Differential Equations, 2005(136), pp. 1-14.

Rights

Attribution 4.0 International

Rights Holder

Rights License