On difference splitting schemes for the Korteweg-de Vries equation

The convergence of difference splitting schemes for the solution of the Korteweg-de Vries equation is considered. A method is developed for obtaining convergence bounds in C for the case when the scheme does not satisfy the maximum, principle. The proposed method is applied to prove convergence theorems for splitting schemes with sufficiently smooth initial values.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 56–61, 1985.