Mathematics and Its Applications series. xvii, 290 p. 24 cm. Hardcover. Ex library with labels on spine and inside rear cover, ink stamps on top edge and title. Small dents in bottom edges.

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Bibliographic Details

Title

Partial Differential Equations: New Methods for their Treatment and Solution

Publisher

D. Reidel Publishing Company, Dordrecht

Publication Date

1985

ISBN 10

9027716811

ISBN 13

9789027716811

Binding

Hardcover

Condition

ex library-good

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Science

About this title

Synopsis

The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non� linear cases even for strong nonlinearities, and also for deterministic or stochastic cases - again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations.

Review

`As a rich source of ideas the text should be highly recommended to mature students in appropriate fields and to research workers.'
Zentralblatt f�r Mathematik (1986)

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