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Numerical Investigation of Spiral Structure Solutions of a Nonlinear Elliptic Problem

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Numerical Methods and Applications (NMA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6046))

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Abstract

The nonlinear elliptic problem considered arises when investigating a class of self-similar solutions of a reaction-diffusion equation. We focus our study on the solutions of spiral structure. The proposed approach is based on the continuous analog of the Newton’s method and on the Galerkin finite element method. To reveal solutions of spiral structure appropriate initial approximations are used. The last ones are expressed by the confluent hypergeometric function 1 F 1(a,b;z). Algorithms for accurate, fast and reliable computation of its values for broad ranges of the parameters a and b and of the variable z are worked out. A detailed numerical analysis of the evolution of the spiral structure solutions with respect to the medium parameters, including critical values, is carried out.

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Dimova, M., Dimova, S. (2011). Numerical Investigation of Spiral Structure Solutions of a Nonlinear Elliptic Problem. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_47

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  • DOI: https://doi.org/10.1007/978-3-642-18466-6_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18465-9

  • Online ISBN: 978-3-642-18466-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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