Electron. J. Diff. Eqns., Vol. 2005(2005), No. 136, pp. 1-14.

Residual models for nonlinear partial differential equations

Garry Pantelis

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.

Submitted November 14, 2005. Published November 30, 2005.
Math Subject Classifications: 35G20, 35G25, 53D10, 93A30.
Key Words: Partial differential equations; nonlinear evolution; contact manifolds; mathematical modelling.

An addendum was posted on July 2, 2007. Some equations are rewritten to clarify their meaning. Please see the last page of this manuscript.

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Garry Pantelis
Department of Computer Science, Intercollege
P. O. Box 42572, 6500 Larnaca, Cyprus
email: pantelis.g@adm.lar.intercol.edu

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