Higher-order incremental unknowns, hiearchical basis, and nonlinear dissipative evolutionary equations (Q1917435)
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scientific article; zbMATH DE number 897523
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Higher-order incremental unknowns, hiearchical basis, and nonlinear dissipative evolutionary equations |
scientific article; zbMATH DE number 897523 |
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Higher-order incremental unknowns, hiearchical basis, and nonlinear dissipative evolutionary equations (English)
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16 March 1997
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The main purpose of the paper is to study the long-term dynamic behavior of nonlinear dissipative evolutionary equations by means of finite difference approximations with several levels of discretization. The main tool is the methodology of the so called ``higher-order incremental unknowns'', which allows the numerical scheme to retain the inherent dissipative property. Two models are discussed: The one-dimensional Kuramoto-Sivashinsky equation of 4th-order in \(x\), with periodic boundary condition, and the two-dimensional Burgers-like equation. The paper concludes with the results of some numerical experiments on the model problems.
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hierarchical basis
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nonlinear dissipative evolutionary equations
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finite difference
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incremental unknowns
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Kuramoto-Sivashinsky equation
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Burgers-like equation
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numerical experiments
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