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Comparison of a Rothe-Two Grig Method and Other Numerical Schemes for Solving Semilinear Parabolic Equations

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Numerical Analysis and Its Applications (NAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3401))

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Abstract

A technique combined the Rothe method with two-grid (coarse and fine) algorithm of Xu [18] for computation of numerical solutions of nonlinear parabolic problems with various boundary conditions is presented. For blow-up solutions we use a decreasing variable step in time, according to the growth of the solution. We give theoretical results, concerning convergence of the numerical solutions to the analytical ones. Numerical experiments for comparison the accuracy of the algorithm with other known numerical schemes are discussed.

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Author information

Authors and Affiliations

  1. Center of Applied Mathematics and Informatics, University of Rousse, 8 Studentska str., Rousse, 7017, Bulgaria

    Miglena N. Koleva

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  1. Miglena N. Koleva
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Editors and Affiliations

  1. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, P.O. Box, Hong Kong

    Zhilin Li

  2. Department of Mathematics, University of Rousse, 7017, Rousse, Bulgaria

    Lubin Vulkov

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

    Jerzy Waśniewski

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© 2005 Springer-Verlag Berlin Heidelberg

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Koleva, M.N. (2005). Comparison of a Rothe-Two Grig Method and Other Numerical Schemes for Solving Semilinear Parabolic Equations. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_42

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  • DOI: https://doi.org/10.1007/978-3-540-31852-1_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24937-5

  • Online ISBN: 978-3-540-31852-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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