Implementation of a Wiener Chaos Expansion Method for the Numerical Solution of the Stochastic Generalized Kuramoto-Sivashinsky Equation Driven by Brownian Motion Forcing
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Bibliographic record
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 $O(\varsigma t)$, where $\varsigma$ is 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.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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