Open Access

ARTICLE

A Meshless Method for Solving the 2D Brusselator Reaction-Diffusion System

by M. Mohammadi¹, R. Mokhtari², R. Schaback⁴

1 Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Ave., Tehran 1561836314, Iran.
2 Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran.
3 Corresponding author.
4 Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestraße 16-18, D-37073 Göttingen, Germany.

Computer Modeling in Engineering & Sciences 2014, 101(2), 113-138. https://doi.org/10.3970/cmes.2014.101.113

Abstract

In this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by the method of lines. The proposed method is implemented as a meshless method based on spatial trial functions in the reproducing kernel Hilbert spaces. For efficiency and stability reasons, we use the Newton basis introduced recently by Müller and Schaback. The method is shown to work in all interesting situations described by Hopf bifurcations and Turing patterns.

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Keywords

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