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Generalized Nonstandard Numerical Methods for Nonlinear Advection-Diffusion-Reaction Equations

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Large-Scale Scientific Computing (LSSC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2907))

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Abstract

A time-splitting method for nonlinear advection-diffusion-reaction equations is formulated and analyzed. The nonlinear advection-reaction part of the problem is solved using a new generalized nonstandard method based on a Lagrangian formulation and a linearizing map. The diffusion part is handled with standard finite difference schemes. This approach leads to significant qualitative improvements in the behavior of the numerical solutions.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Texas at Arlington, 19408, Arlington, TX, 76019-0408, USA

    Hristo V. Kojouharov

  2. Department of Mathematics, Arizona State University, P.O. Box 871804, Tempe, AZ, 85287-1804, USA

    Bruno D. Welfert

Authors
  1. Hristo V. Kojouharov
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  2. Bruno D. Welfert
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

  4. Center of Applied Mathematics and Informatics, University of Rousse, 7017, Rousse, Bulgaria

    Plamen Yalamov

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© 2004 Springer-Verlag Berlin Heidelberg

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Kojouharov, H.V., Welfert, B.D. (2004). Generalized Nonstandard Numerical Methods for Nonlinear Advection-Diffusion-Reaction Equations. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_53

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  • DOI: https://doi.org/10.1007/978-3-540-24588-9_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21090-0

  • Online ISBN: 978-3-540-24588-9

  • eBook Packages: Springer Book Archive

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