Title

Quantitative measurement of variational approximations

Authors

Authors

D. J. Kaup;T. K. Vogel

Comments

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Abbreviated Journal Title

Phys. Lett. A

Keywords

NONLINEAR SCHRODINGER-EQUATION; PRINCIPLE; SOLITON; INSTABILITIES; DYNAMICS; Physics, Multidisciplinary

Abstract

Variational problems have long been used to mathematically model physical systems. Their advantage has been the simplicity of the model as well as the ability to deduce information concerning the functional dependence of the system on various parameters embedded in the variational trial functions. However, the only method in use for estimating the error in a variational approximation has been to compare the variational result to the exact solution. In this Letter, we demonstrate that one can computationally obtain estimates of the errors in a one-dimensional variational approximation, without any a priori knowledge of the exact solution. Additionally, this analysis can be done by using only linear techniques. The extension of this method to multidimensional problems is clearly possible, although one could expect that additional difficulties could arise. (c) 2007 Elsevier B.V. All rights reserved.

Journal Title

Physics Letters A

Volume

362

Issue/Number

4

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

289

Last Page

297

WOS Identifier

WOS:000244975300011

ISSN

0375-9601

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