Solving Frontier Problems of Physics

The Decomposition Method

By: G. Adomian

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Hardcover | 31 December 1993

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372 Pages

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23.5 x 16.51 x 2.54

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The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems.
This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches.
The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted.
For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.

Industry Reviews

`I recommend Adomian's new book to all researchers in the area of mathematical modeling and solving complex dynamical systems.'
Foundations of Physics, 1994

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Non-Fiction Science Physics Mathematical Physics Mathematics Probability & Statistics Calculus & Mathematical Analysis Differential Calculus & Equations Applied Mathematics Science in General Maths for Scientists

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Published: 9th December 2010

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Preface
Foreword
On Modelling Physical Phenomena	p. 1
The Decomposition Method for Ordinary Differential Equations	p. 6
The Decomposition Method in Several Dimensions	p. 22
Double Decomposition	p. 69
Modified Decomposition	p. 115
Applications of Modified Decomposition	p. 154
Decomposition Solutions for Neumann Boundary Conditions	p. 190
Integral Boundary Conditions	p. 196
Boundary Conditions at Infinity	p. 211
Integral Equations	p. 224
Nonlinear Oscillations in Physical Systems	p. 228
Solution of the Duffing Equation	p. 236
Boundary-Value Problems With Closed Irregular Contours Or Surfaces	p. 288
Applications in Physics	p. 302
Appendix I. Pade and Shanks Transforms	p. 338
Appendix II. On Staggered Summation of Double Decomposition Series	p. 348
Appendix III. Cauchy Products of Infinite Series	p. 350
Index	p. 352
Table of Contents provided by Blackwell. All Rights Reserved.

Solving Frontier Problems of Physics

The Decomposition Method

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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