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

Victor Nijimbere, Carleton University, Ottawa, Ontario, Canada
2019 Journal of Advances in Applied Mathematics  

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2019 pre-print
arXiv:1910.03022v1 fatcat:lyt27r73h5fs5oiiclj3si5unq
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(ς t), where ς is small constant and t
more » ... 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.
doi:10.22606/jaam.2019.44001 fatcat:jswufr7pfbffhjnhu45ra4ocfa
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Victor Nijimbere, Carleton University, Ottawa, Ontario, Canada. "Implementation of a Wiener Chaos Expansion Method for the Numerical Solution of the Stochastic Generalized Kuramoto-Sivashinsky Equation Driven by Brownian Motion Forcing." Journal of Advances in Applied Mathematics 4.4 (2019)