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International Workshop on Computer Algebra in Scientific Computing

CASC 2014: Computer Algebra in Scientific Computing pp 432–446Cite as

CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of the Burgers and Korteweg–de Vries–Burgers Equations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8660))

Abstract

In the present work, the computer algebra system (CAS) is applied for constructing a new version of the analytic-numerical method of collocations and least residuals (CLR) for solving the Burgers equation and the Korteweg–de Vries–Burgers equation. The CAS is employed at all stages from writing, deriving, and verifying the formulas of the method to their translation into arithmetic operators of the Fortran language. The verification of derived formulas of the method has been done on the test problem solutions. Comparisons of the results of numerical computations by the new CLR method with the exact solutions of test problems show a high accuracy of the developed method.

The work was partially supported by the Russian Foundation for Basic research (grant No. 13-01-00277).

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Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Vasily P. Shapeev & Evgenii V. Vorozhtsov

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  1. Vasily P. Shapeev
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  2. Evgenii V. Vorozhtsov
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, 34132, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Shapeev, V.P., Vorozhtsov, E.V. (2014). CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of the Burgers and Korteweg–de Vries–Burgers Equations. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_31

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  • DOI: https://doi.org/10.1007/978-3-319-10515-4_31

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10514-7

  • Online ISBN: 978-3-319-10515-4

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