Download or read book Stability and Instability Exact and Approximate Solutions of Linear Differential Equations with Time Varying Coefficients written by Alfonso Fred Ratcliffe and published by . This book was released on 1970 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The familiar soluble linear differential equations and the properties of linear systems are reviewed. The importance of linear differential equations and the origins of some such problems are discussed. The exact solutions of a class of second order differential equations and a more general class of nth order equations - those for which the fundamental solution matrix is composed of orthogonal vectors - are derived. A canonical form and the transformation, which leads to it, are derived and from this canonical form conclusions are drawn with respect to stability or instability using a modification of Liapounov stability theory. The canonical form dx/dt = (lambda + N)x where lambda is a diagonal matrix and N is an nxn skew symmetric matrix, is subsequently used to obtain approximate solutions to both homogeneous and nonhomogeneous linear differential equations. While the methods of this dissertation may theoretically be applied to an nth order linear system, in practice they are limited to second and third order systems unless machines are used. (Author).

Download or read book Stability and Instability written by A. F. Ratcliffe and published by . This book was released on 1970 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Differential Equations with Variable Coefficients written by Ĭosip Zakharovych Shtokalo and published by . This book was released on 1961 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1988 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximate Solution of Linear Differential Equations written by C. T. Leondes and published by . This book was released on 1970 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The approximate solution of linear differential equations, both homogeneous and nonhomogeneous, is investigated for systems with time varying coefficients. In particular, those systems which are asymptotically stable are investigated and quadratic error measures are defined as means of choosing the particular simple and soluble approximating systems which replace the original insoluble or difficult system. (Author).

Download or read book The Solution of Linear Differential Equations with Time varying Coeffecients by an Approximate Operational Method written by Robert N. Parker and published by . This book was released on 1956 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Numerical Methods for Time Dependent Differential Equations written by Heinz-Otto Kreiss and published by John Wiley & Sons. This book was released on 2014-04-24 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

Download or read book Approximate Solution in a Finite Time Interval for Ordinary Nonlinear Differential Equations written by Robert Ernest Lindsay and published by . This book was released on 1962 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this investigation is to obtain approximate solutions over finite time intervals to ordinary, nonlinear, differential equations. A new method of approximation is introduced which, for a given differential equation and associated initial conditions, yields an approximate solution which is close to the exact solution everywhere in the prescribed time interval. Because of the nature of the approximate solution, an estimate of the solution error can be obtained from the original differential equation. This approximation technique is compared with some well-known method of approximation. Examples are considered in which the approximation method developed in this research gives superior numerical results. Further, problem areas are indicated (multiple-degree-of-freedom systems, timevariable systems) which are not suitable for treatment by some of the well-known methods but capable of analysis by the technique to be presented in this study. (Author).

Download or read book Stability and Instability of Time Varying Linear Systems written by C. T. Leondes and published by . This book was released on 1970 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear systems with time varying coefficients are examined and a canonical form of the governing differential equation is proposed which possesses certain advantageous properties: Stability or instability may be concluded by inspection in some cases; Conservative estimates of the stability or instability of second and third order systems may be obtained in many practical cases. (Author).

Download or read book Stability Periodic Solutions of Ordinary Functional Differential Equations written by T. A. Burton and published by Courier Corporation. This book was released on 2014-06-24 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.

Download or read book Transient and Nonlinear Effects on High Speed Vibratory Thermoelastic Instability Phenomena written by Eugene J. Brunelle (Jr.) and published by . This book was released on 1960 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Exact Solutions for Ordinary Differential Equations written by Valentin F. Zaitsev and published by CRC Press. This book was released on 2002-10-28 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo

Download or read book Current Challenges in Stability Issues for Numerical Differential Equations written by Wolf-Jürgen Beyn and published by Springer. This book was released on 2013-12-12 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies. Topics considered include: (i) the long time integration of Hamiltonian Ordinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionary partial DEs, (iv) decomposition of matrices depending on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs. The problems considered in this volume are of interest to people working on numerical as well as qualitative aspects of differential equations, and it will serve both as a reference and as an entry point into further research.

Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Download or read book Stability Instability and Chaos written by Paul Glendinning and published by Cambridge University Press. This book was released on 1994-11-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.

Download or read book Ordinary Differential Equations and Stability Theory written by David A. Sánchez and published by Courier Corporation. This book was released on 1979-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a general discussion of the linear equation, topics developed include stability theory for autonomous and nonautonomous systems. Two appendices are also provided, and there are problems at the end of each chapter — 55 in all. Unabridged republication of the original (1968) edition. Appendices. Bibliography. Index. 55 problems.

Download or read book Stability Theory of Differential Equations written by Richard Bellman and published by Courier Corporation. This book was released on 2013-02-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.