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Nonlinear Stochastic Operator Equations
1st Edition - December 28, 1986
Author: George Adomian
9 7 8 - 1 - 4 8 3 2 - 5 9 0 9 - 3
Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of… Read more
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Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case), which yield results very different from the needs of the actual physical problem. Real-world application of mathematics to actual physical problems, requires making a reasonable model that is both realistic and solvable. The decomposition approach or model is an approximation method to solve a wide range of problems. This book explains an inherent feature of real systems—known as nonlinear behavior—that occurs frequently in nuclear reactors, in physiological systems, or in cellular growth. This text also discusses stochastic operator equations with linear boundary conditions. This book is intended for students with a mathematics background, particularly senior undergraduate and graduate students of advanced mathematics, of the physical or engineering sciences.
Chapter 1 Introduction
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 y10 Term of the Decomposition for Initial or Boundary Conditions
Suggested Further Reading
Chapter 3 Expansion of Nonlinear Terms: The An Polynomials
3.2. Calculation of the An Polynomials for Simple Nonlinear Operators
3.3. 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