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Lattice Boltzmann Model for Nonlinear Heat Equations

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Book cover Advances in Neural Networks – ISNN 2012 (ISNN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7367))

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Abstract

In this paper, a lattice Boltzmann scheme with an amending function for the nonlinear heat equations with the form ∂  t φ = α ∇ 2 φ + ψ(φ) which directly to solve some important nonlinear equations, including Fisher equation, Newell-Whitehead equation and FitzHugh-Nagumo equation is proposed . Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions or the numerical solutions reported in previous studies.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, P.R. China

    Qiaojie Li, Zhoushun Zheng, Shuang Wang & Jiankang Liu

Authors
  1. Qiaojie Li
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  2. Zhoushun Zheng
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  3. Shuang Wang
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  4. Jiankang Liu
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Editor information

Editors and Affiliations

  1. Department of Mechanical & Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    Jun Wang

  2. School of Electrical and Computer Engineering, Oklahoma State University, 74078, Stillwater, OK, USA

    Gary G. Yen

  3. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, 1678, Nicosia, Cyprus

    Marios M. Polycarpou

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© 2012 Springer-Verlag Berlin Heidelberg

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Li, Q., Zheng, Z., Wang, S., Liu, J. (2012). Lattice Boltzmann Model for Nonlinear Heat Equations. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_17

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  • DOI: https://doi.org/10.1007/978-3-642-31346-2_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31345-5

  • Online ISBN: 978-3-642-31346-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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