Solving Frontier Problems of Physics: The Decomposition Method
Series: Fundamental Theories of Physics; 60;
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Product details:
- Edition number 1994
- Publisher Springer Netherlands
- Date of Publication 31 December 1993
- Number of Volumes 1 pieces, Book
- ISBN 9780792326441
- Binding Hardback
- No. of pages354 pages
- Size 234x156 mm
- Weight 1540 g
- Language English
- Illustrations XIV, 354 p. Illustrations, black & white 0
Categories
Long description:
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.
Table of Contents:
1 On Modelling Physical Phenomena.- 2 The Decomposition Method for Ordinary Differential Equations.- 3 The Decomposition Method in Several Dimensions.- 4 Double Decomposition.- 5 Modified Decomposition.- 6 Applications of Modified Decomposition.- 7 Decomposition Solutions for Neumann Boundary Conditions.- 8 Integral Boundary Conditions.- 9 Boundary Conditions at Infinity.- 10 Integral Equations.- 11 Nonlinear Oscillations in Physical Systems.- 12 Solution of the Duffing Equation.- 13 Boundary-Value Problems with Closed Irregular Contours or Surfaces.- 14 Applications in Physics.- Appendix I Padé and Shanks Transforms.- Appendix II On Staggered Summation of Double Decomposition Series.- Appendix III Cauchy Products of Infinite Series.
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