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Equadiff 82 pp 93–100Cite as

Numerical analysis of singularities in a diffusion reaction model

Part of the Lecture Notes in Mathematics book series (LNM,volume 1017)

Abstract

In a recent paper, Bigge and Bohl [2] found some interesting bifurcation diagrams for a discrete diffusion reaction model. We give an interpretation of their results from the view of singularity theory and we will also indicate how this theory may be used to set up numerical methods for singular solutions such as bifurcation points or isolated points.

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References

  1. Beyn, W.-J.: On discretizations of bifurcation problems. pp. 46–73 in Bifurcation problems and their numerical solution (Eds.: H.D. Mittelmann, H. Weber), ISNM 54, Birkhäuser Verlag, 1980.

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  2. Bigge, J., Bohl, E.: On the steady states of finitely many chemical cells (submitted).

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  3. Bohl, E.: Finite Modelle gewöhnlicher Randwertaufgaben. LAMM Bd. 51, Teubner Verlag, Stuttgart, 1981.

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  4. Golubitsky, M., Guillemin, V.: Stable mappings and their singularities. Graduate Texts in Mathematics No. 14, Springer Verlag, New York, 1974.

    MATH  Google Scholar 

  5. Golubitsky, M., Schaeffer, D.: A theory for imperfect bifurcation via singularity theory. Commun. Pure Appl. Math. 32, 21–98, 1979.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Martinet, J.: Deploiements versels des applications differentiables et classification des applications stables. pp. 1–44, Lecture Notes in Mathematics 535, Springer Verlag, 1976.

    Google Scholar 

  7. Moore, G.: The numerical treatment of non-trivial bifurcation points. Numer. Funct. Anal. Optimiz. 2, 441–472, 1980.

    CrossRef  MATH  Google Scholar 

  8. Poston, T., Stewart, I.: Catastrophe theory and its applications. Pitman, London, 1978.

    MATH  Google Scholar 

  9. Vainberg, M.M., Trenogin, V.A.: The methods of Lyapunov and Schmidt in the theory of non-linear equations and their further development. Russian Math. Surveys 17, 1–60, 1962.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Weber, H.: On the numerical approximation of secondary bifurcation points. pp. 407–425, Lecture Notes in Mathematics 878, Springer Verlag, 1981.

    Google Scholar 

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© 1983 Springer-Verlag

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Beyn, W.J. (1983). Numerical analysis of singularities in a diffusion reaction model. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103239

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  • DOI: https://doi.org/10.1007/BFb0103239

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12686-7

  • Online ISBN: 978-3-540-38678-0

  • eBook Packages: Springer Book Archive