Journal of Mathematical Chemistry

, Volume 43, Issue 4, pp 1533–1548

Wavelet approach incorporated with optimization for solving stiff systems

  • Tonghua Zhang
  • Moses O. Tadé
  • Yu-Chu Tian
  • Yanduo Zhang
  • Johan Utomo
Original Paper

DOI: 10.1007/s10910-007-9282-2

Cite this article as:
Zhang, T., Tadé, M.O., Tian, YC. et al. J Math Chem (2008) 43: 1533. doi:10.1007/s10910-007-9282-2
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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.

Wavelet-based methodWavelet-Galerkin methodConnection coefficientsStiff systemNumerical solutionDaubechies wavelet

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Tonghua Zhang
    • 1
  • Moses O. Tadé
    • 1
  • Yu-Chu Tian
    • 2
  • Yanduo Zhang
    • 3
  • Johan Utomo
    • 1
  1. 1.Department of Chemical EngineeringCurtin University of TechnologyPerthAustralia
  2. 2.School of Software Engineering and Data Communications, Faculty of Information TechnologyQueensland University of TechnologyBrisbaneAustralia
  3. 3.School of Computer Science and EngineeringWuhan Institute of TechnologyWuhanP.R. China