Ebook: Group Invariance in Engineering Boundary Value Problems
Author: R. Seshadri T. Y. Na (auth.)
- Tags: Analysis, Mechanical Engineering, Engineering Design
- Year: 1985
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Integrals . . . . . . " 193 . 11.4 Reduction of Number of Variables by Multiparameter Groups of Transformations . . . . . . . . .. . . . 194 11.5 Self-Similar Solutions of the First and Second Kind . . 202 11.6 Normalized Representation and Dimensional Consideration 204 REFERENCES .206 Problems . 208 .220 Index .. Chapter 1 INTRODUCTION AND GENERAL OUTLINE Physical problems in engineering science are often described by dif ferential models either linear or nonlinear. There is also an abundance of transformations of various types that appear in the literature of engineer ing and mathematics that are generally aimed at obtaining some sort of simplification of a differential model.
Content:
Front Matter....Pages i-ix
Introduction and General Outline....Pages 1-4
Concepts of Continuous Transformation Groups....Pages 5-34
A Survey of Methods for Determining Similarity Transformations....Pages 35-61
Application of Similarity Analysis to Problems in Science and Engineering....Pages 62-90
Similarity Analysis of Boundary Value Problems with Finite Boundaries....Pages 91-102
On Obtaining Non-Similar Solutions from Similar Solutions....Pages 103-124
Moving Boundary Problems Governed by Parabolic Equations....Pages 125-136
Similarity Analysis of Wave Propagation Problems....Pages 137-156
Transformation of a Boundary Value Problem to an Initial Value Problem....Pages 157-168
From Nonlinear to Linear Differential Equations using Transformation Groups....Pages 169-189
Miscellaneous Topics....Pages 190-207
Back Matter....Pages 208-224
Content:
Front Matter....Pages i-ix
Introduction and General Outline....Pages 1-4
Concepts of Continuous Transformation Groups....Pages 5-34
A Survey of Methods for Determining Similarity Transformations....Pages 35-61
Application of Similarity Analysis to Problems in Science and Engineering....Pages 62-90
Similarity Analysis of Boundary Value Problems with Finite Boundaries....Pages 91-102
On Obtaining Non-Similar Solutions from Similar Solutions....Pages 103-124
Moving Boundary Problems Governed by Parabolic Equations....Pages 125-136
Similarity Analysis of Wave Propagation Problems....Pages 137-156
Transformation of a Boundary Value Problem to an Initial Value Problem....Pages 157-168
From Nonlinear to Linear Differential Equations using Transformation Groups....Pages 169-189
Miscellaneous Topics....Pages 190-207
Back Matter....Pages 208-224
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