Group Invariance in Engineering Boundary Value Problems

1. Front Matter

   Pages i-ix

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2. Introduction and General Outline

   • R. Seshadri, T. Y. Na

   Pages 1-4

3. Concepts of Continuous Transformation Groups

   • R. Seshadri, T. Y. Na

   Pages 5-34

4. A Survey of Methods for Determining Similarity Transformations

   • R. Seshadri, T. Y. Na

   Pages 35-61

5. Application of Similarity Analysis to Problems in Science and Engineering

   • R. Seshadri, T. Y. Na

   Pages 62-90

6. Similarity Analysis of Boundary Value Problems with Finite Boundaries

   • R. Seshadri, T. Y. Na

   Pages 91-102

7. On Obtaining Non-Similar Solutions from Similar Solutions

   • R. Seshadri, T. Y. Na

   Pages 103-124

8. Moving Boundary Problems Governed by Parabolic Equations

   • R. Seshadri, T. Y. Na

   Pages 125-136

9. Similarity Analysis of Wave Propagation Problems

   • R. Seshadri, T. Y. Na

   Pages 137-156

10. Transformation of a Boundary Value Problem to an Initial Value Problem

    • R. Seshadri, T. Y. Na

    Pages 157-168

11. From Nonlinear to Linear Differential Equations using Transformation Groups

    • R. Seshadri, T. Y. Na

    Pages 169-189

12. Miscellaneous Topics

    • R. Seshadri, T. Y. Na

    Pages 190-207

13. Back Matter

    Pages 208-224

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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.

• Boundary
• Boundary value problem
• Engineering
• Group
• Invariance
• partial differential equation
• translation

• Syncrude Canada Limited, Fort McMurray, Canada

  R. Seshadri

• Department of Mechanical Engineering, University of Michigan—Dearborn, Dearborn, USA

  T. Y. Na

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