Download or read book Similarity Solutions for Partial Differential Equations Generated by Finite and Infinitesimal Groups written by Henry Stott Woodard and published by . This book was released on 1971 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of developing systematic methods for obtaining similarity variables is considered for partial differential equations. Similarity variables are a set of transformations which reduce a partial differential equation to an ordinary differential equation. This paper considers two methods of generating similarity variables. The first method uses a group of finite transformations and the second uses a group of infinitesimal transformations. The mathematical theory for both techniques is described and illustrated. The two methods of obtaining similarity variables are applied to the Burgers' equation u(sub y) + u(u sub x) = u sub xx and to the laminar boundary layer equations with a pressure gradient. In all cases considered, new types of similarity variables are found. In addition, the auxiliary conditions are discussed in the light of the new similarity variables obtained for the boundary layer equations. (Author).

Download or read book Similarity Solutions for Partial Differential Equations Generated by Finite and Infinitesimal Groups written by Henry Stott Woodard (Jr.) and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Similarity Solutions of Nonlinear Partial Differential Equations written by Lawrence Dresner and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Group Analysis of Differential Equations written by L. V. Ovsiannikov and published by Academic Press. This book was released on 2014-05-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.

Download or read book Nonlinear Partial Differential Equations in Engineering by W F Ames written by W. F. Ames and published by Elsevier. This book was released on 1972-07-21 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

Download or read book Similarity Analyses of Partial Differential Equations written by Tsung Yen Na and published by . This book was released on 1967 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book NBS Special Publication written by and published by . This book was released on 1973 with total page 1562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Selected Library Acquisitions written by United States. Department of Transportation and published by . This book was released on with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Group Invariance in Engineering Boundary Value Problems written by R. Seshadri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1980 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Download or read book Hydraulic Research in the United States and Canada written by United States. National Bureau of Standards and published by . This book was released on 1972 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Mechanics Update written by and published by . This book was released on 1986 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Classed Subject Catalog written by Engineering Societies Library and published by . This book was released on 1972 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Physics and Physical Mathematics written by Instytut Matematyczny (Warschau) and published by Springer. This book was released on 1976-09-30 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Symposium organized by the Mathematical Institute of the Polish Academy of Sciences, The Institute for Nuclear Research, Warsaw, 25-30 March 1974

Download or read book Hydraulic Research in the United States and Canada 1972 written by Gershon Kulin and published by . This book was released on 1974 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics in Science and Engineering written by and published by . This book was released on 1972 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: