Abstract
The Korteweg-de Vries equation is numerically solved by using the Fourier expansion method, the finite-difference methods, and other methods. By applying each method to a common initial-value problem, the accuracies of computations are compared with each other. The Fourier expansion method is found to be the most accurate and effective method. The details of the recurrence of an initial state, discussed by N. J. Zabusky and M. D. Kruskal, are examined.
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