The Method of Fractional Steps The Solution of Problems of Mathemati
The method of. fractional steps, known familiarly as the method oi splitting, is a remarkable technique, developed by N. N. Yanenko and his collaborators, for solving problems in theoretical mechanics numerically. It is applicable especially to potential
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The Method of Fractional Steps The Solution of Problems of Mathematical Physics in Several Variables
English Translation Editetl by M. Holt
With 15 Figures
Springer-Verlag Berlin Heidelberg New York 1971
Professor N. N. Yanenko U.S.S.R. Academy of Sciences, Siberian Branch Computing Center, Novosibirsk, U.S.S.R.
Professor Maurice Holt University of California, Berkeley, Cal., U.S.A.
Translated into English by Northrop Corporate Laboratories, Hawthorne, Cal., U.S.A.
ISBN-13 :978-3-642-6511 0-6 e-ISBN-13 :978-3-642-651 08-3 DOl: lO.lO07! 978-3-642-65lO8-3 Title of the Russian Original Edition: Metod drobnykh shagov resheniya rnnogomernykh zadach matematicheskoi fiziki Publisher: "Nauka", Sibirskoe Otdelenie, Novosibirsk 1967 Title of the French Translation: Methode it pas fractionnaires, resolutions de problemes polydimensionnels de physique mathematique. Librairie Armand Colin, Paris 1968 Title of the German Translation: Die Zwischenschrittmethode zur Lasung mehrdimensionaler Probleme der mathematischen Physik (Lecture Notes in Mathematics, Vol. 91), 1969 ISBN-13 :978-3-642-65110-6
This work js subject to copyright. All rights are reserved, whether the whole or pari of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data j::>anks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag, Berlin· Heidelberg 1971. Library of Congress Catalog Card Number 78-139953 Softcover reprint of the hardcover 1st edition 1971
Editor's Preface The method of. fractional steps, known familiarly as the method oi splitting, is a remarkable technique, developed by N. N. Yanenko and his collaborators, for solving problems in theoretical mechanics numerically. It is applicable especially to potential problems, problems of elasticity and problems of fluid dynamics. Most of the applications at the present time have been to incompressible flow with free boundaries and to viscous flow at low speeds. The method offers a powerful means of solving the Navier-Stokes equations and the results produced so far cover a range of Reynolds numbers far greater than that attained in earlier methods. Further development of the method should lead to complete numerical solutions of many of the boundary layer and wake problems which at present defy satisfactory treatment. As noted by the author very few applications of the method have yet been made to problems in solid mechanics and prospects for answers both in this field and other areas such as heat transfer are encouraging. As the method is perfected it is likely to supplant traditional relaxation methods and finite element methods, especially with the increase in capability of large scale computers. The literal translation was carried out by T. Cheron with financial support of the Northrop Corporation. T
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