Nonlinear Problems of Engineering

William F. Ames

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9781483200781
• eBook ISBN: 9781483225814
• Topic: Physical Sciences
• Subtopic: Energy

Nonlinear Problems of Engineering reviews certain nonlinear problems of engineering. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena. Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This text then explores nonlinear integral equations, which have long occupied a prominent place in mathematical analysis. Other chapters consider the phenomena associated with essentially divergent small-divisor series, such as may occur in the formal solution of differential equations that represent the oscillations of conservative dynamical systems. This book discusses as well the mechanics of idealized textiles consisting of inextensible filaments. The final chapter deals with the use of the Peaceman–Rachford alternating direction implicit method for solving the finite difference analogs of boundary value problems. This book is a valuable resource for engineers and mathematicians.

Table of contents

• Front Cover
• Nonlinear Problems of Engineering
• Copyright Page
• Table of Contents
• Contributors
• Foreword
• Preface
• Chapter 1. New Methods in Nonlinear Mechanics
• Chapter 2. Probability as a Science
• Chapter 3. On Random Solutions of Nonlinear Integral Equations
• Chapter 4. A Singular Case of Iteration of Analytic Functions: A Contribution to the Small-Divisor Problem
• Chapter 5 . Networks of Inextensible Cords
• Chapter 6. On Integral Operators Generating Stream Functions of Compressible Fluids
• Chapter 7. Some Problems Concerning Linear Differential Equations Made Nonlinear by Unknown or Moving Boundaries
• Chapter 8. Nonlinear Problems of Combined Conductive-Radiative Heat Transfer
• Chapter 9. Statistical Problems Connected with the Solution of a Nonlinear Partial Differential Equation
• Chapter 10. Melting Decelerating Bodies
• Chapter 11. Thermal Radiation Effects on Hypersonic Flow Fields
• Chapter 12. Mathematical Theory of Compressible Fluids
• Chapter 13. Problems in Nonlinear Nonmechanics
• Chapter 14. Nonlinear Problems in Ballistics
• Chapter 15. Alternating Direction Methods for Solving Partial Difference Equations
• Subject Index