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.

Solving Frontier Problems of Physics: The Decomposition Method (Fundamental Theories of Physics) PDF

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