Journal
APPLIED MATHEMATICAL MODELLING
Volume 34, Issue 12, Pages 3896-3909Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2010.03.028
Keywords
Two-dimensional reaction-diffusion; Brusselator system; Collocation method; Radial basis functions (RBFs); Stability analysis
Funding
- HEC, Islamabad [041-303216/M-112]
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This paper studies a meshfree technique for the numerical solution of the two-dimensional reaction-diffusion Brusselator system along with Dirichlet and Neumann boundary conditions. Combination of collocation method using the radial basis functions (RBFs) with first order accurate forward difference approximation is employed for obtaining meshfree solution of the problem. Different types of RBFs are used for this purpose. The method is shown to converge to the only equilibrium point of the system. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the results obtained from the existing methods [7,8]. The elementary stability analysis is established theoretically and is also supported by numerical results. (C) 2010 Elsevier Inc. All rights reserved.
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