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Iterative Solution of Linear and Nonlinear Boundary Problems Using PIES

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Book cover Parallel Processing and Applied Mathematics (PPAM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6067))

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Abstract

The paper presents an effective approach to solving boundary problems modeled by a nonlinear partial differential equation. An applied algorithm bases on: an iterative method used in order to find successive approximations to the solution of a boundary problem and PIES method as a tool for solving a boundary problem in each iteration step. The paper also contains some suggestions about an effective way of domains modeling and calculation of integrals over those domains. Authors also have performed an initial verification of a method on the basis of a linear equation and nonlinear equations with a various intensity of nonlinearity.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Bialystok, Sosnowa 64, 15-887, Bialystok, Poland

    Eugeniusz Zieniuk & Agnieszka Boltuc

Authors
  1. Eugeniusz Zieniuk
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  2. Agnieszka Boltuc
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Editor information

Editors and Affiliations

  1. Institute of Computational and Information Sciences, Czestochowa University of Technology,  

    Roman Wyrzykowski

  2. Department of Electrical Engineering and Computer Science, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Dabrowskiego 73, PL-42-200, Czestochowa, Poland

    Konrad Karczewski

  4. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Wasniewski

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Zieniuk, E., Boltuc, A. (2010). Iterative Solution of Linear and Nonlinear Boundary Problems Using PIES. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14390-8_15

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  • DOI: https://doi.org/10.1007/978-3-642-14390-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14389-2

  • Online ISBN: 978-3-642-14390-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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