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Immersed Interface Method for a Reaction-Diffusion Equation with a Moving Own Concentrated Source

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

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Abstract

An Immersed Interface Method (IIM) is developed for a reaction-diffusion problem with discontinuous coefficients and a moving own singular source. On a regular grid using Crank-Nicolson method a second order difference scheme is constructed. Numerical examples, which confirm theoretical analysis, are discussed.

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References

  1. Beyer, R., Leveque, R.:Analysis of a one-dimensional model for the immersed boundary method. SIAM J. Numer. Anal. 29 (1992) 332–364.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bimpong-Bota, K., Nizan, A., Ortoleva, P., Ross, J.: Cooperative phenomena in analysis of catalytic sites. J. Chem. Phys. 66 (1970) 3650–3683.

    Article  Google Scholar 

  3. Kandilarov, J.: A second-order difference method for solution of diffusion problems with localized chemical reactions. In: Samarskii A.A., Vabishchevich P. N., Matus P. P. (eds.): Proceed. of Second Int. Conf. Finite Difference Methods: Theory and Applications. Minsk (1999) 63–67.

    Google Scholar 

  4. Kandilarov, J., Vulkov, L.: The immersed interface method for a nonlinear chemical diffusion equation with local sites of reactions. (submitted).

    Google Scholar 

  5. Li, Z.: Immersed interface method for moving interface problems. Numer. Algorithms, 14 (1997) 269–293.

    Article  MATH  MathSciNet  Google Scholar 

  6. Pierce, A., Rabitz, H.: An analysis of the effect of defect structures on catalytic surfaces by the boundary element technique. Surface Science, 202 (1988) 1–31.

    Article  Google Scholar 

  7. Samarskii, A.: The Theory of Difference Schemes. Nauka, Moscow (1977) (in Russian)

    Google Scholar 

  8. Samarskii, A., Friazinov, I.: Convergence of a homogeneous difference schemes for heat equation with discontinuous coefficients. Comput. Math. and Math. Phys. 1 (1961) 806–824.

    Google Scholar 

  9. Vabishchevich, P., Matus, P., Richagov, V.: On a class of difference schemes locally refined grids. Differ. Uravn. 31, 5 (1995) 849–857.

    Google Scholar 

  10. Vulkov, L., Kandilarov, J.: Construction and implementation of finite-difference schemes for systems of diffusion equations with localized chemical reactions. Comp. Math. Math. Phys. 40, 5 (2000) 705–717.

    MATH  Google Scholar 

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Authors and Affiliations

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

    Juri D. Kandilarov

Authors
  1. Juri D. Kandilarov
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Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

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© 2003 Springer-Verlag Berlin Heidelberg

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Kandilarov, J.D. (2003). Immersed Interface Method for a Reaction-Diffusion Equation with a Moving Own Concentrated Source. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_57

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  • DOI: https://doi.org/10.1007/3-540-36487-0_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

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