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Spectral collocation method for stochastic Burgers equation driven by additive noise

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  • Kamrani, Minoo
  • Hosseini, S. Mohammad

Abstract

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differential equations (SODEs). The resulting SODEs system is then solved by an explicit 3-stage stochastic Runge-Kutta method of strong order one. The convergence rate of Fourier collocation method for Burgers equation is also obtained. Some numerical experiments are included to show the performance of the method.

Suggested Citation

  • Kamrani, Minoo & Hosseini, S. Mohammad, 2012. "Spectral collocation method for stochastic Burgers equation driven by additive noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1630-1644.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:9:p:1630-1644
    DOI: 10.1016/j.matcom.2012.03.007
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    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    2. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
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