A fast spectral algorithm for nonlinear wave equations with linear dispersion
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.
Adams-Bashforth and Adams-Moulton methods
scientific article; zbMATH DE number 1384948