Overview
- Authors:
-
-
Richard Bellman
-
Dept. of Electrical Engineering, University of Southern California, Los Angeles, USA
Center for Applied Mathematics, The University of Georgia, Athens, USA
-
George Adomian
-
Center for Applied Mathematics, The University of Georgia, Athens, USA
Access this book
Other ways to access
Table of contents (19 chapters)
-
Front Matter
Pages i-xvii
-
- Richard Bellman, George Adomian
Pages 1-4
-
- Richard Bellman, George Adomian
Pages 5-27
-
- Richard Bellman, George Adomian
Pages 28-35
-
- Richard Bellman, George Adomian
Pages 36-58
-
- Richard Bellman, George Adomian
Pages 59-61
-
- Richard Bellman, George Adomian
Pages 62-81
-
- Richard Bellman, George Adomian
Pages 82-87
-
- Richard Bellman, George Adomian
Pages 88-102
-
- Richard Bellman, George Adomian
Pages 103-109
-
- Richard Bellman, George Adomian
Pages 110-119
-
- Richard Bellman, George Adomian
Pages 120-128
-
- Richard Bellman, George Adomian
Pages 129-147
-
- Richard Bellman, George Adomian
Pages 148-152
-
- Richard Bellman, George Adomian
Pages 153-175
-
- Richard Bellman, George Adomian
Pages 176-236
-
- Richard Bellman, George Adomian
Pages 237-242
-
- Richard Bellman, George Adomian
Pages 243-247
-
- Richard Bellman, George Adomian
Pages 248-253
-
- Richard Bellman, George Adomian
Pages 254-288
About this book
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.
Reviews
`As a rich source of ideas the text should be highly recommended to mature students in appropriate fields and to research workers.'
Zentralblatt für Mathematik (1986)
