The Numerical Solution Of Some Problems In Continuum Mechanics Involving Two Point Boundary Conditions
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Numerical Solution of Two Point Boundary Value Problems
| Author | : Herbert B. Keller |
| Publisher | : SIAM |
| Total Pages | : 69 |
| Release | : 1976-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970449 |
Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Free Boundary Problems in Continuum Mechanics
| Author | : S.N. Antontsev |
| Publisher | : Birkhäuser |
| Total Pages | : 348 |
| Release | : 2013-03-07 |
| Genre | : Science |
| ISBN | : 3034886276 |
Progress in different fields of mechanics, such as filtra tion theory, elastic-plastic problems, crystallization pro cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have convened, since the 1980s, in such countries as England, the United states, Italy, France and Germany. This book comprises the papers presented at the Interna tional Conference "Free Boundary Problems in Continuum Mechanics", organized by the Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, July 15-19, 1991, Novosibirsk, Russia. The scientific committee consisted of: Co-chairmen: K.-H. Hoffmann, L.V. Ovsiannikov S. Antontsev (Russia) J. Ockendon (UK) M. Fremond (France) L. Ovsiannikov (Russia) A. Friedman (USA) S. Pokhozhaev (Russia) K.-H. Hoffmann (Germany) M. Primicerio (Italy) A. Khludnev (Russia) V. Pukhnachov (Russia) V. Monakhov (Russia) Yu. Shokin (Russia) V. Teshukov (Russia) Our thanks are due to the members of the Scientific Com mittee, all authors, and participants for contributing to the success of the Conference. We would like to express special appreciation to N. Makarenko, J. Mal'tseva and T. Savelieva, Lavrentyev Institute of Hydrodynamics, for their help in preparing this book for publication
The Numerical Solution of Two-point Boundary Problems in Ordinary Differential Equations
| Author | : Leslie Fox |
| Publisher | : Courier Dover Publications |
| Total Pages | : 0 |
| Release | : 1990 |
| Genre | : Boundary value problems |
| ISBN | : 9780486664958 |
Accessible, undergraduate-level treatment devoted exclusively to boundary-value problems. Detailed numerical techniques for equations of orders up to 4, for simultaneous equations and for eigenvalue problems. Includes numerous examples. Bibliographies.
A First Course in Ordinary Differential Equations
| Author | : Martin Hermann |
| Publisher | : Springer Science & Business |
| Total Pages | : 300 |
| Release | : 2014-04-22 |
| Genre | : Mathematics |
| ISBN | : 8132218353 |
This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.
On the Numerical Solution of Two-point Boundary Value Problems
| Author | : Yale University. Department of Computer Science |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 1989 |
| Genre | : Boundary value problems |
| ISBN | : |
Abstract: "In this paper, we present a new numerical method for the solution of linear two-point boundary value problems of ordinary differential equations. After reducing the differential equation to a second kind integral equation, we discretize the latter via a high order Nyström scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O(N [multiplied by] p[superscript 2]) operations, where N is the number of nodes on the interval and p is the desired order of convergence. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to end-point singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods."
Meshless Methods in Solid Mechanics
| Author | : Youping Chen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 211 |
| Release | : 2006-12-31 |
| Genre | : Science |
| ISBN | : 0387333681 |
This book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.
Problems of Nonlinear Deformation
| Author | : E.I. Grigolyuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 270 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 9401137765 |
Interest in nonlinear problems in mechanics has been revived and intensified by the capacity of digital computers. Consequently, a question offundamental importance is the development of solution procedures which can be applied to a large class of problems. Nonlinear problems with a parameter constitute one such class. An important aspect of these problems is, as a rule, a question of the variation of the solution when the parameter is varied. Hence, the method of continuing the solution with respect to a parameter is a natural and, to a certain degree, universal tool for analysis. This book includes details of practical problems and the results of applying this method to a certain class of nonlinear problems in the field of deformable solid mechanics. In the Introduction, two forms of the method are presented, namely continu ous continuation, based on the integration of a Cauchy problem with respect to a parameter using explicit schemes, and discrete continuation, implementing step wise processes with respect to a parameter with the iterative improvement of the solution at each step. Difficulties which arise in continuing the solution in the neighbourhood of singular points are discussed and the problem of choosing the continuation parameter is formulated.
Numerical Methods in Fluid Dynamics
| Author | : M. Holt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 262 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642963706 |
This monograph is based on a graduate course, Mechanical Engipeering 266, which was developed over a number of years at the University of California-Berkeley. Shorter versions of the course were given at the University of Paris VI in 1969, and at the University of Paris XI in 1972. The course was originally presented as the last of a three quarter sequence on Compressible Flow Theory, with emphasis on the treatment of non-linear problems by numerical techniques. This is reflected in the material of the first half of the book, covering several techniques for handling non-linear wave interaction and other problems in Gas Dynamics. The techniques have their origins in the Method of Characteristics (in both two and three dimensions). Besides reviewing the method itself the more recent techniques derived from it, firstly by Godunov and his group, and secondly by Rusanov and his co-workers, are described. Both these approaches are applicable to steady flows calculated as asymptotic states of unsteady flows and treat elliptic prob lems as limiting forms of unsteady hyperbolic problems. They are there fore applicable to low speed as well a~ to high speed flow problems. The second half of the book covers the treatment of a variety of steady flow problems, including effects of both viscosity and compressibi lity, by the Method of Integral Relations, Telenin's Method, and the Method of Lines.
