Group invariance in engineering boundary value problems

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書誌事項

Group invariance in engineering boundary value problems

R. Seshadri, T.Y. Na

Springer-Verlag, c1985

大学図書館所蔵 件 / 全17件

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注記

Includes bibliographies and index

内容説明・目次

内容説明

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 .2 06 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.

目次

1 Introduction and General Outline.- References.- 2 Concepts of Continuous Transformation Groups.- 2.0 Introduction.- 2.1 Group Approach.- 2.2 Transformation Groups.- 2.3 The Concept of an Infinitesimal Transformation.- 2.4 Relation Between Global and Infinitesimal Groups Transformations.- 2.5 The Concept of Invariance.- 2.6 Invariance of Differential Equations Under Groups of Transformations.- 2.7 The Extended Group of Transformations.- 2.8 The Characteristic Function.- 2.9 Transformations Involving Two Independent Variables.- 2.10 Transformation Involving Two Dependent and Two Independent Variables.- 2.11 Dimensional and Affine Groups of Transformations.- 2.12 Summary.- References.- 3 A Survey of Methods for Determining Similarity.- 3.0 Introduction.- 3.1 Direct Methods.- 3.2 Group-Theoretic Methods.- 3.3 Summary.- References.- 4 Application of Similarity Analysis to Problems in Sciences and Engineering.- 4.0 Introduction.- 4.1 Laminar Two Dimensional Jet:Separation of Variable Method.- 4.2 Impact of Rods With Nonlinear Material Properties: Separation of Variables Method.- 4.3 Diffusion of Vorticity From a Line Vortex Immersed in a Quiescent Fluid: Dimensional Method.- 4.4 Laminar Boundary Layer Equation: Dimensional Method.- 4.5 Free Convection From a Vertical Needle: Heliums Churchill Method.- 4.6 Deflection of a Semi-Infinite Wedge Shaped Plate: Birkhoff-Morgan Method.- 4.7 Heated Jet: Birkhoff-Morgan Method.- 4.8 Unsteady One-Dimensional Gas Dynamics Equations: Characteristic Function Method.- 4.9 Summary.- References.- 5 Similarity Analysis of Boundary Value Problems With Finite Boundaries.- 5.0 Introduction.- 5.1 Boundary Value Problems With Moving Boundaries.- 5.2 Invariant Boundary and Surface Description.- 5.3 Invariance Under Groups Other Than Dimensional Groups.- 5.4 Summary.- References.- 6 On Obtaining Non-Similar Solutions From Similar Solutions.- 6.0 Introduction.- 6.1 Superposition of Similarity Solutions.- 6.2 The Use of Fundamental Solutions.- 6.3 Pseudo-Similarity Transformations.- 6.4 Similarity Solutions as Asymptotic Limits of the Non-Similar Problem Description.- 6.5 Summary.- References.- 7 Moving Boundary Problems Governed by Parabolic Equations.- 7.0 Introduction.- 7.1 Problems With Phase Change.- 7.2 Problems Without Phase Change.- 7.3 Summary.- References.- 8 Similarity Analysis of Wave Propagation Problems.- 8.0 General.- 8.1 Propagation Along Characteristics.- 8.2 Non-Characteristic Propagation:Shock Waves.- 8.3 Non-Characteristic Propagation:Uniform Propagation Regime.- 8.4 From Translation to Dimensional Group Invariance.- 8.5 Summary.- References.- 9 Transformation of a Boundary Value Problem to an Initial Value Problem.- 9.0 Introduction.- 9.1 Blasius Equation in Boundary Layer Flow.- 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods.- 9.3 Summary.- References.- 10 From Nonlinear to Linear Differential Equations Using Transformation Groups.- 10.1 From Nonlinear to Linear Differential Equations.- 10.2 Application to Ordinary Differential Equations Bernoulli's Equation.- 10.3 Application to Partial Differential Equations A Nonlinear Chemical Exchange Process.- 10.4 Limitations of the Inspectional Group Method.- 10.5 Summary.- References.- 11 Miscellaneous Topics.- 11.1 Reduction of Differential Equations to Algebraic Equations.- 11.2 Reduction of Order of an Ordinary Differential Equation.- 11.3 Transformation From Ordinary to Partial Differential Equations-Search for First Integrals.- 11.4 Reduction of Number of Variables by Multiparameter Groups of Transformations.- 11.5 Self-Similar Solutions of the First and Second Kind.- 11.6 Normalized Representation and Dimensional Consideration.- References.- Problems.

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