Kansa method for the solution of a parabolic equation with an unknown spacewise-dependent coefficient subject to an extra measurement

Parabolic partial differential equations with an unknown spacewise-dependent coefficient serve as models in many branches of physics and engineering. Recently, much attention has been expended in studying these equations and there has been a considerable mathematical interest in them. In this work,...

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Bibliographic Details
Published in:Computer physics communications 2013-03, Vol.184 (3), p.582-595
Main Authors: Parand, K., Rad, J.A.
Format: Article
Language:English
Subjects:
Cartesian nodes
Coefficients
Computer simulation
Convergence
Errors
Exact solutions
Heat source
Inverse problem
Mathematical analysis
Mathematical models
Meshless methods
One-dimensional parabolic equation
Radial basis functions
Random noise
Specifications
Stability analysis
Unknown spacewise-dependent coefficient
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Summary:Parabolic partial differential equations with an unknown spacewise-dependent coefficient serve as models in many branches of physics and engineering. Recently, much attention has been expended in studying these equations and there has been a considerable mathematical interest in them. In this work, the solution of the one-dimensional parabolic equation is presented by the method proposed by Kansa. The present numerical procedure is based on the product model of the space–time radial basis function (RBF), which was introduced by Myers et al. Using this method, a rapid convergent solution is produced which tends to the exact solution of the problem. The convergence of this scheme is accelerated when we use the Cartesian nodes as center nodes. The accuracy of the method is tested in terms of Error and RMS errors. Also, the stability of the technique is investigated by perturbing the additional specification data by increasing the amounts of random noise. The numerical results obtained show that the proposed method produces a convergent and stable solution.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2012.10.012