Skip to main content

Numerical Simulations of Reaction-Diffusion Systems Arising in Chemistry Using Exponential Integrators

  • Conference paper
Large-Scale Scientific Computing (LSSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5910))

Included in the following conference series:

  • 2192 Accesses

Abstract

We perform a comparative numerical study of two reaction-diffusion models arising in chemistry by using exponential integrators. Numerical simulations of the reaction kinetics associated with these models, including both the local and global errors as a function of time step and error as a function of computational time are shown.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Ashkenazi, M., Othmer, H.G.: Spatial Patterns in Coupled Biochemical Oscillators. J. Math. Biol. 5, 305–350 (1978)

    MATH  MathSciNet  Google Scholar 

  2. Berland, H., Skaflestad, B.: Solving the nonlinear Schrödinger equation using exponential integrators. Modeling, Identification and Control 27(4), 201–217 (2006)

    Article  Google Scholar 

  3. Berland, H., Skaflestad, B., Wright, W.: EXPINT — A Matlab package for exponential integrators. Numerics 4 (2005)

    Google Scholar 

  4. Butcher, J.C.: Numerical methods for ordinary differential equations. John Wiley & Sons, Chichester (2003)

    Book  MATH  Google Scholar 

  5. Celledoni, E., Marthinsen, A., Qwren, B.: Commutator-free Lie group methods. FGCS 19(3), 341–352 (2003)

    Google Scholar 

  6. Cox, S.M., Matthews, P.C.: Exponential time differencing for stiff systems. J. Comp. Phys. 176(2), 430–455 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kepper, P., De Castets, V., Dulos, E., Boissonade, J.: Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction. Physica D 49, 161–169 (1991)

    Article  Google Scholar 

  8. Krogstad, S.: Generalized integrating factor methods for stiff PDEs. Journal of Computational Physics 203(1), 72–88 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lawson, D.J.: Generalized Runge-Kutta processes for stable systems with large Lipschitz constants. SIAM J. Numer. Anal. 4, 372–380 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lengyel, I., Epstein, I.R.: Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system. Science 251, 650–652 (1991)

    Article  Google Scholar 

  11. Minchev, B., Wright, W.M.: A review of exponential integrators for semilinear problems. Technical Report 2, The Norwegian University of Science and Technology (2005)

    Google Scholar 

  12. Munthe-Kaas, H.: High order Runge-Kutta methods on manifolds. Applied Numerical Mathematics 29, 115–127 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Nørsett, S.P.: An A-stable modification of the Adams-Bashforth methods. In: Conf. on Numerical solution of Differential Equations, Dundee, pp. 214–219. Springer, Berlin (1969)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ştefănescu, R., Dimitriu, G. (2010). Numerical Simulations of Reaction-Diffusion Systems Arising in Chemistry Using Exponential Integrators. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_74

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12535-5_74

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12534-8

  • Online ISBN: 978-3-642-12535-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics