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Adomian G. — Solving Frontier Problems of Physics: The Decomposition Method
Adomian G. — Solving Frontier Problems of Physics: The Decomposition Method



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Название: Solving Frontier Problems of Physics: The Decomposition Method

Автор: Adomian G.

Аннотация:

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.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 351

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(Adomian) polynomials reference list      11
Acceleration techniques      30 206 338
Analytic simulants      17 289
Applications of modified decomposition      154
Applications, advection      316
Applications, advection-diffusion      318
Applications, Burger's equation      311
Applications, dissipative wave equation      28 30
Applications, KdV equation      321
Applications, Kuramoto — Sivashinsky equation      312
Applications, Lane — Emden equation      315
Applications, n-body problem      328
Applications, Navier — Stokes equation      302
Applications, nonlinear heat equation      322
Applications, nonlinear Klein — Gordon equation      322
Applications, nonlinear relativistic partial differential equation      334
Applications, nonlinear transport in moving fluids      316
Applications, random nonlinear heat equation      323
Applications, Schroedinger equation, nonlinear      327
Applications, Schroedinger equation, quartic potential      325
Applications, Schroedinger equation, Yukawa-coupled Klein — Gordon      327
Applications, Sine — Gordon equation      324
Applications, turbulence      307
Applications, Van der Pol equation      230 231 309
Asymptotic decomposition      18 241
Boundary conditions at infinity      211
Boundary-value problems      87 114 138 288
Cauchy products      350
Convergence regions      23 25
Decomposition for ordinary differential equations      6 28
Decomposition for partial differential equations      22 28
Difficult nonlinearities      150
Dirichlet conditions      75
Double decomposition      22 69 87
Duffing equation      154 157 230 231 235 236 263 277 280
Generalized (Adomian) polynomials      50
Generalized Taylor series      10
Gibbs phenomena      301
harmonic oscillator      247 251
Integral boundary conditions      196
Integral equations      224
Irregular contours or surfaces      288
Mixed derivatives      46
Modified decomposition      115 131 138 214
Neumann boundary conditions      190
Noise terms      29
Nonlinear ordinary differential equations      85
Nonlinear oscillations      228
Nonlinear partial differential equations      80
Partial solutions      23 28 30 32 35 36
Perturbation      284
Proliferation of terms      254
Smooth expansions of piecewise-differentiable functions      298
Spatial and temporal formats      97 106 109
Staggered summation      243 348
Stopping rules      18
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