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Group Invariance in Engineering Boundary Value Problems

  • R. Seshadri
  • T. Y. Na

Table of contents

  1. Front Matter
    Pages i-ix
  2. R. Seshadri, T. Y. Na
    Pages 1-4
  3. R. Seshadri, T. Y. Na
    Pages 5-34
  4. R. Seshadri, T. Y. Na
    Pages 103-124
  5. R. Seshadri, T. Y. Na
    Pages 125-136
  6. R. Seshadri, T. Y. Na
    Pages 137-156
  7. R. Seshadri, T. Y. Na
    Pages 190-207
  8. Back Matter
    Pages 208-224

About this book

Introduction

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.

Keywords

Boundary Boundary value problem Engineering Group Invariance partial differential equation translation

Authors and affiliations

  • R. Seshadri
    • 1
  • T. Y. Na
    • 2
  1. 1.Syncrude Canada LimitedFort McMurrayCanada
  2. 2.Department of Mechanical EngineeringUniversity of Michigan—DearbornDearbornUSA

Bibliographic information