Convergence of Galerkin approximations for the Korteweg-de Vries equation

Baker, Garth A.; Dougalis, Vassilios A.; Karakashian, Ohannes A.

doi:10.1090/S0025-5718-1983-0689464-4

Convergence of Galerkin approximations for the Korteweg-de Vries equation

Authors: Garth A. Baker, Vassilios A. Dougalis and Ohannes A. Karakashian
Journal: Math. Comp. 40 (1983), 419-433
MSC: Primary 65M60; Secondary 65M10
DOI: https://doi.org/10.1090/S0025-5718-1983-0689464-4
MathSciNet review: 689464
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Abstract: Standard Galerkin approximations, using smooth splines on a uniform mesh, to 1-periodic solutions of the Korteweg-de Vries equation are analyzed. Optimal rate of convergence estimates are obtained for both semidiscrete and second order in time fully discrete schemes. At each time level, the resulting system of nonlinear equations can be solved by Newton's method. It is shown that if a proper extrapolation is used as a starting value, then only one step of the Newton iteration is required.

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