A high-order fully discrete scheme for the Korteweg–de Vries equation with a time-stepping procedure of Runge–Kutta-composition type

Autor:	Angel Durán, Vassilios A. Dougalis
Rok vydání:	2021
Předmět:	Discretization Applied Mathematics General Mathematics Order (ring theory) Type (model theory) Space (mathematics) Mathematics::Numerical Analysis Computational Mathematics Runge–Kutta methods Scheme (mathematics) Applied mathematics Korteweg–de Vries equation Midpoint method Mathematics
Zdroj:	IMA Journal of Numerical Analysis. 42:3022-3057
ISSN:	1464-3642 0272-4979
DOI:	10.1093/imanum/drab060
Popis:	We consider the periodic initial-value problem for the Korteweg–de Vries equation that we discretize in space by a spectral Fourier–Galerkin method and in time by an implicit, high-order, Runge–Kutta scheme of composition type based on the implicit midpoint rule. We prove $L^{2}$ error estimates for the resulting semidiscrete and the fully discrete approximations. Some numerical experiments illustrate the results.
Databáze:	OpenAIRE
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