Nonlinear Partial Differential Equations

A Symposium on Methods of Solution

W. F. Ames

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9781483196473
• eBook ISBN: 9781483221502
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.

Table of contents

• Front Cover
• Nonlinear Partial Differential Equations: A Symposium on Methods of Solution
• Copyright Page
• Table of Contents
• List of Contributors
• Foreword
• Preface
• Chapter 1. Generalized Similarity Analysis of Partial Differential Equations
• Chapter 2. Vector Eigenfunction Expansions for the Growth of Taylor Vortices in the Flow between Rotating Cylinders
• Chapter 3. New Methods for the Solution of Partial Differential Equations
• Chapter 4. Ad hoc Exact Techniques for Nonlinear Partial Differential Equations
• Chapter 5. The Lubrication Approximation Applied to Non-Newtonian Flow Problems: A Perturbation Approach
• Chapter 6. The Computation of Compressible Boundary-Layer Flow
• Chapter 7. Integral Equations for Nonlinear Problems in Partial Differential Equations
• Chapter 8. Electrical Problems Modeled by Nonlinear Partial Differential Equations
• Chapter 9. Difference Methods and Soft Solutions
• Chapter 10. Numerical Solution of the Nonlinear Equations for Two-Phase Flow through Porous Media
• Chapter 11. An Extrapolated Crank-Nicolson Difference Scheme for Quasilinear Parabolic Equations
• Chapter 12. Heat Transfer to the Endwall of a Shocktube. A Variational Analysis
• Chapter 13. A Synergetic Approach to Problems of Nonlinear Dispersive Wave Propagation and Interaction
• Chapter 14. Uniformization of Asymptotic Expansions
• Chapter 15. High Order Accurate Difference Methods in Hydrodynamics
• Chapter 16. Nonlinear Problems in the Dynamics of Thin Shells
• Index