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A fast spectral algorithm for nonlinear wave equations with linear dispersion. (English) Zbl 0937.65109
The authors presented an easily implemented time stepping strategy for spatially spectral numerical solution to a wide range of nonlinear wave equations. The methods combine Adams-Bashforth and Adams-Moulton methods for the nonlinear and stiff linear parts, respectively, with the novel feature that different methods are used in different wavenumber ranges. The result combines high temporal accuracy with good stability properties. Numerical tests conducted on the Korteweg-de Vries and nonlinear Schrödinger equations show that the new approach is computationally more effective than other currently available methods.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
Software:
RODAS
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