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＜電子ブック＞
Group Invariance in Engineering Boundary Value Problems / by R. Seshadri, T.Y. Na

版	1st ed. 1985.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1985
本文言語	英語
大きさ	224 p : online resource
著者標目	*Seshadri, R author Na, T.Y author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mechanical engineering LCSH:Engineering design FREE:Analysis FREE:Mechanical Engineering FREE:Engineering Design
一般注記	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-SimilarSolutions of the First and Second Kind -- 11.6 Normalized Representation and Dimensional Consideration -- References -- Problems 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 HTTP:URL=https://doi.org/10.1007/978-1-4612-5102-6

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