Fourier pseudospectral methods for generalized symmetric regularized long wave equations (Q2719608)
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scientific article; zbMATH DE number 1609807
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier pseudospectral methods for generalized symmetric regularized long wave equations |
scientific article; zbMATH DE number 1609807 |
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25 June 2001
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generalized symmetric regularized long wave equations
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Fourier pseudospectral schemes
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initial periodic boundary value problem
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convergence
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optimal error estimate
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Fourier pseudospectral methods for generalized symmetric regularized long wave equations (English)
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The authors study the Fourier pseudospectral method approximation for the generalized symmetric regularized long wave equations [cf. \textit{C. E. Seyler} and \textit{D. C. Fanstermacher}, Phys. Fluids, 27, 4-7 (1984; Zbl 0544.76170)]: \(u_t-u_{xxt}+\rho_x+\varphi (u)_x=f(u)\), \(\rho_t +u_x =g(\rho)\) with initial and periodic boundary conditions. The authors construct semi-discrete and fully-discrete schemes. Using the (discrete) energy estimates, the authors prove the convergence of the schemes provided that the solutions are smooth enough. Moreover, an optimal error estimate for \(u\) in \(H^1\)-norm and for \(\rho\) in \(L^2\)-norm is presented. This paper generalizes some related results.
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0.8859074115753174
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0.8781102299690247
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