Quantitative measurement of variational approximations

    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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