Front Cover; Nonlinear Stochastic Operator Equations; Copyright Page; Table of Contents; Foreword; Preface; Acknowledgments; Chapter 1. Introduction; References; Chapter 2. Operator Equations and the Decomposition Method; 2.1. Modeling, Approximation, and Reality; 2.2. The Operator Equations; 2.3. The Decomposition Method; 2.4. Evaluation of the Inverse Operator L-1 and the y0 Term of the Decomposition for Initial or BoundaryConditions; References; Suggested Further Reading; Chapter 3. Expansion of Nonlinear Terms: The AnPolynomials; 3.1. Introduction.

3.2. Calculation of the An Polynomials for Simple Nonlinear Operators3.3. The An Polynomials for Differential Nonlinear Operators; 3.4. Convenient Computational Forms for the An Polynomials; 3.5. Linear Limit; 3.6. Calculation of the An Polynomials for Composite Nonlinearities; References; Suggested Further Reading; Chapter 4. Solution of Differential Equations; 4.1. General Method and Examples; 4.2. Calculating a Simple Green's Function; 4.3. Green's Function by Decomposition; 4.4. Approximating Difficult Green's Functions; 4.5. Polynomial Nonlinearities; 4.6. Negative Power Nonlinearities.

4.7. Decimal Power Nonlinearities4.8. Product Nonlinearities; 4.9. Anharmonic Oscillator Systems; 4.10. Limiting Case: The Harmonic Oscillator; 4.11. Extensions to Stochastic Oscillators; 4.12. Asymptotic Solutions; 4.13. The Question of Stability; References; Chapter 5. Coupled Nonlinear Stochastic Differential Equations; 5.1. Deterministic Coupled Differential Equations; 5.2. Stochastic Coupled Equations; 5.3. Generalization to n Coupled Stochastic Differential Equations; Suggested Further Reading; Chapter 6. Delay Equations; 6.1. Definitions; 6.2. Solution of Delay Operator Equations.

9.6. Inhomogeneous Heat Equation9.7. Asymptotic Decomposition for Partial Differential Equations; Note; Reference; Suggested Further Reading; Chapter 10. Algebraic Equations; Part I: Polynomials; 10.1. Quadratic Equations by Decomposition; 10.2. Cubic Equations; 10.3. Higher-Degree Polynomial Equations; 10.4. Equation with Negative Power Nonlinearities; 10.5. Equations with Noninteger Powers; 10.6. Equations with Decimal Powers; 10.7. Random Algebraic Equations; 10.8. General Remarks; Part II: Transcendental Equations; 10.9. Trigonometric Equations; 10.10. Exponential Cases; 10.11. Logarithmic Equation: Purely Nonlinear Equations; Nonlinear Stochastic Operator Equations.