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The problems of ocean dynamics present more and more com plex tasks
for investigators, based on the continuously sophisti cation of
theoretical models, which are applied with the help of universal
and efficient algorithms of numerical mathematics. The present
level of our knowledge in the field of mathemat ical physics and
numerical mathematics allows one to give rather complete
theoretical analysis of basic statements of problems as well as
numerical algorithms. Our task is to perform such analy sis and
also to analyze the results of calculations in order to improve our
knowledge of the mechanism of large-scale hy drological processes
occurring in the World Ocean. The new level of numerical
mathematics has essentially influenced, the formation of new
solution methods of ocean dynamics prob lems, among which an
important one is the splitting method, which has been already
widely practised in various fields of science and engineering. A
number of monographs by N. N. Yanenko, A. A. Samarsky, G. . Marchuk
(Rozhdestvensky and Yanenko 1968; Samarsky and Andreyev 1976;
Marchuk 1970, 1980b) and others are devoted to the description of
this methods. But the methods of the splitting theory require
extensive creative work for their application to concrete problems,
which are peculiar, as a rule, in problem formulation. The success
of the application of these methods is related to the deep
understanding of the essence of the described processes. In the
last decades fundamental works of Arakawa, K."
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