Nonlinear stochastic systems theory and applications to physics

George Adomian


  • I: A Summary of the Decomposition Method.- 1: The Decomposition Method.- 1.1 Introduction.- 1.2 Summary of the Decomposition Method.- 1.3 Generation of the An Polynomials.- 1.4 The An for Differential Nonlinear Operators.- 1.5 Convenient Computational Forms for the An Polynomials.- 1.6 Calculation of the An Polynomials for Composite Nonlinearities.- 1.7 New Generating Schemes - the Accelerated Polynomials.- 1.8 Convergence of the An Polynomials.- 1.9 Euler's Transformation.- 1.9.1 Solution of a Differential Equation by Decomposition.- 1.9.2 Application of Euler Transform to Decomposition Solution.- 1.9.3 Numerical Comparison.- 1.9.4 Solution of Linearized Equation.- 1.10 On the Validity of the Decomposition Solution.- 2: Effects of Nonlinearity and Linearization.- 2.1 Introduction.- 2.2 Effects on Simple Systems.- 2.3 Effects on SOlution for the General Case.- 3: Research on Initial and Boundary Conditions for Differential and Partial Differential Equations.- II: Applications to the Equations of Physics.- 4: The Burger's Equation.- 5: Heat Flow and Diffusion.- 5.1 One-Dimensional Case.- 5.2 Two-Dimensional Case.- 5.3 Three-Dimensional Case.- 5.4 Some Examples.- 5.5 Heat Conduction in an Inhomogeneous Rod.- 5.6 Nonlinear Heat Conduction.- 5.7 Heat Conduction Equation with Discontinuous Coefficients.- 5.8 Nonlinear Boundary Conditions.- 5.9 Comparisons.- 5.10 Uncoupled Equations with Coupled Conditions.- 6: Nonlinear Oscillations in Physical Systems.- 6.1 Oscillatory Motion.- 6.2 Pendulum Problem.- 6.3 The Duffing and Van der Pol Oscillators.- 7: The KdV Equation.- 8: The Benjamin-Ono Equation.- 9: The Sine-Gordon Equation.- 10: The Nonlinear Schrodinger Equation and the Generalized Schrodinger Equation.- 10.1 Nonlinear Schrodinger Equation.- 10.2 Generalized Schrodinger Equation.- 10.3 Schrodinger's Equation with a Quartic Potential.- 11: Nonlinear Plasmas.- 12: The Tricomi Problem.- 13: The Initial-Value Problem for the Wave Equation.- ChaDter 14: Nonlinear Dispersive or Dissipative Waves.- 14.1 Wave Propagation in Nonlinear Media.- 14.2 Dissipative Wave Equations.- 15: The Nonlinear Klein-Gordon Equation.- 16: Analysis of Model Equations of Gas Dynamics.- 17: A New Approach to the Efinger Model for a Nonlinear Quantum Theory for Gravitating Particles.- 18: The Navier-Stokes Equations.- Epilogue.

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書名 Nonlinear stochastic systems theory and applications to physics
著作者等 Adomian, G.
Adomian George
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic Publishers
刊行年月 c1989
ページ数 xx, 224 p.
大きさ 25 cm
ISBN 902772525X
NCID BA06505987
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言語 英語
出版国 オランダ