Journal of Mathematical Chemistry

, Volume 44, Issue 2, pp 501–513 | Cite as

Wavelet-based collocation method for stiff systems in process engineering

Original Paper


Abrupt phenomena in modelling real-world systems such as chemical processes indicate the importance of investigating stiff systems. However, it is difficult to get the solution of a stiff system analytically or numerically. Two such types of stiff systems describing chemical reactions were modelled in this paper. A numerical method was proposed for solving these stiff systems, which have general nonlinear terms such as exponential function. The technique of dealing with the nonlinearity was based on the Wavelet-Collocation method, which converts differential equations into a set of algebraic equations. Accurate and convergent numerical solutions to the stiff systems were obtained. We also compared the new results to those obtained by the Euler method and 4th order Runge–Kutta method.


Wavelet Collocation method Stiff system Numerical solution Chemical reaction model 


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  1. 1.
    Bertoluzza S., Naldi G. (1996). A wavelet collocation method for the numerical solution of partial differential equations, Appl. Comput. Harm. Anal. 3, 1–9CrossRefGoogle Scholar
  2. 2.
    Chen M., Hwang C., Shih Y. (1996) The computation of wavelet-galerkin approximation on a bounded interval, Int. J. Numer. Methods Eng. 39, 2921–2944CrossRefGoogle Scholar
  3. 3.
    Daubechies I. (1992) Ten Lectures on Wavelets. SIAM, PhiladelphiaGoogle Scholar
  4. 4.
    Hsiao C.H. (2004) Haar wavelet approach to linear stiff systems. Math. Comput. Simu. 64, 561–567CrossRefGoogle Scholar
  5. 5.
    Liu Y., Tadé M.O. (2004) New wavelet-based adaptive method for the breakage equation. Powder Technol. 139, 61–68CrossRefGoogle Scholar
  6. 6.
    S.W. Ravindra, S.M. Arun, Optimal non-isothermal reactor network for Van de Vusse reaction, Int. J. Chem. React. Eng. 3, 1–18 (2005) ( Scholar
  7. 7.
    Rice R.G., Do D.D. (1994) Appl. Math. & Model. Chem. Eng. John Wiley & Sons, Inc., New YorkGoogle Scholar
  8. 8.
    Riggs J.B. (1994) An Introduction to Numerical Methods for Chemical Engineerings, 2nd edn. Texas Tech University Press, USAGoogle Scholar
  9. 9.
    H.H. Robertson, The Solution of a Set of Reaction Rate Equations (Academic Press, 1966), pp. 178–182Google Scholar
  10. 10.
    Zhang T., Tian Y.-C., Tadé M.O., Utomo J. (2007) Comments on “The Computation of Wavelet-Galerkin Approximation on a Bounded Interval”, Int. J. Numer. Meth. Eng. 72, 244–251CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  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

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