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Solving frontier problems of physics: the decomposition method. (English) Zbl 0802.65122
Fundamental Theories of Physics. 60. Dordrecht: Kluwer Academic Publishers. xiii, 352 p. (1994).
The monograph is devoted to the author’s decomposition method, with examples from various fields of mathematical physics, including some frontier problems.
The opening chapters deal with various fundamental aspects of the proposed method, presented by the author also in some previous monographs: Stochastic systems (1983; Zbl 0523.60056) and Nonlinear stochastic operator equations (1986; Zbl 0609.60072). Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffin equation, boundary value problems with closed irregular contours or surfaces, and other frontier areas. Also, the potential application of this method to other problems in diverse disciplines such as biology, geology, hydrology, semiconductor physics, wave propagation, etc. is highlighted.
General nonlinear oscillatory systems and integral equations are also included in the book, to mention but a few. This book can be viewed as a quantitative theory of dynamical systems recommended to researchers and graduate students of physics, mathematics, and engineering as well as to every scientist whose work involves mathematical modeling and the solution of dynamical systems.

65Z05 Applications to the sciences
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65L05 Numerical methods for initial value problems
37-XX Dynamical systems and ergodic theory
35Qxx Partial differential equations of mathematical physics and other areas of application