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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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
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