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Title

Wavelet approach incorporated with optimization for solving stiff systems

Author(s)

Zhang, Tonghua;  Tade, Moses O.;  Tian, Yu-Chu;  Zhang, Yanduo;  Utomo, Johan

Abstract

Wavelet-based methods open a door for numerical solution of differential equations. Stiff systems, a special type of differential equation systems, have the solutions with the components that exhibit complex dynamic behaviours such as singularities and abrupt transitions, which are hard to be captured by the typical numerical method or incur the computing complexity. This paper proposed to use the Wavelet-Galerkin scheme for solving stiff systems. Daubechies wavelet based connection coefficients, required in the Wavelet-Galerkin scheme, were computed using an algorithm that we recently rectified. The Lagrange multiplier method was incorporated into the wavelet approach in order to optimise the fitting of the initial conditions. Comparative studies were also carried out between the proposed approach and the Haar wavelet approach.

Publication type

Journal article

Source

Journal of Mathematical Chemistry, Vol. 43, no. 4 (May 2008), pp. 1533-1548

Publication year

2008

FOR Code(s)

01 Mathematical Sciences;  03 Chemical Sciences

Keyword(s)

Connection coefficients;  Daubechies wavelet;  Numerical solution;  Stiff system;  Wavelet-based method;  Wavelet-Galerkin method

Publisher

Springer

ISSN

0259-9791

Publisher URL

http://dx.doi.org/10.1007/s10910-007-9282-2

Copyright

Copyright © 2007 Springer Science+Business Media, LLC. The accepted manuscript of the paper is reproduced here in accordance with the copyright policy of the publisher. The definitive version of the publication is available at www.springer.com.

Full text

Peer reviewed