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Finite Differences Method for the First Order 2-D Partial Equation

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Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

In this study a new method for finding exact solution of the Cauchy problem subject to a discontinuous initial profile for the two dimensional scalar conservation laws is suggested. For this aim, first, some properties of the weak solution of the linearized equation are investigated. Taking these properties into consideration an auxiliary problem having some advantages over the main problem is introduced. The proposed auxiliary problems also permit us to develop effective different numerical algorithms for finding the solutions. Some computer experiments are carried out.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computing, Beykent University, Sisli-Ayazaga Campus, 34396, Istanbul, Turkey

    Mahir Rasulov

  2. Department of Physics, Yildiz Technical University, Istanbul, Turkey

    E. Ilhan Sahin

  3. Zorlu Holding, Istanbul, Turkey

    M. Gokhan Soguksu

Authors
  1. Mahir Rasulov
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  2. E. Ilhan Sahin
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  3. M. Gokhan Soguksu
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Rasulov, M., Sahin, E.I., Soguksu, M.G. (2013). Finite Differences Method for the First Order 2-D Partial Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_51

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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