Publication Date:
2021-08-12
Description:
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.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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