Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Implementation of a Wiener Chaos Expansion Method for the Numerical Solution of the Stochastic Generalized Kuramoto-Sivashinsky Equation Driven by Brownian Motion Forcing

Download PDF (964.4 KB) PP. 119 - 142 Pub. Date: October 15, 2019

DOI: 10.22606/jaam.2019.44001

Author(s)

  • Victor Nijimbere*
    Carleton University, Ottawa, Ontario, Canada

Abstract

Numerical computations based on the Wiener Chaos Expansion (WCE) are carried out to approximate the solutions of the stochastic generalized Kuramoto–Sivashinsky (SgKS) equation driven by Brownian motion forcing. In the assessment of the accuracy of the WCE based approximate numerical solutions, the WCE based solutions are contrasted with semi-analytical solutions, and the absolute and relative errors are evaluated. It is found that the absolute error is O(ςt), where ς is a small constant and t is the time variabe; and the relative error is order 10−2 or less. This demonstrates that numerical methods based on the WCE are powerful tools to solve the SgKS equation or other related stochastic evolution equations.

Keywords

Wiener Chaos Expansion, semi-analytical solutions, stochastic Kuramoto-Sivashinsky equation, stochastic boundary conditions, error analysis.

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