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.
- ISBN10 3540961283
- ISBN13 9783540961284
- Publish Date 31 December 1985 (first published 12 March 1985)
- Publish Status Out of Print
- Out of Print 11 November 2010
- Publish Country DE
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Format Hardcover
- Pages 224
- Language English