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Approximate Solution In A Finite Time Interval For Ordinary Nonlinear Differential Equations
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Book Synopsis Approximate Solution in a Finite Time Interval for Ordinary Nonlinear Differential Equations by : Stanford University. Stanford Electronics Laboratories
Download or read book Approximate Solution in a Finite Time Interval for Ordinary Nonlinear Differential Equations written by Stanford University. Stanford Electronics Laboratories and published by . This book was released on 1962 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate Solution in a Finite Time Interval for Ordinary Nonlinear Differential Equations by : Robert Ernest Lindsay
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).
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) by : Granville Sewell
Download or read book Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) written by Granville Sewell and published by World Scientific. This book was released on 2014-12-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact.
Book Synopsis Nonlinear Ordinary Differential Equations by : Martin Hermann
Download or read book Nonlinear Ordinary Differential Equations written by Martin Hermann and published by Springer. This book was released on 2016-05-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.
Book Synopsis The Approximation of Solutions on Non-linear Differential Equations by : Melvin D. George
Download or read book The Approximation of Solutions on Non-linear Differential Equations written by Melvin D. George and published by . This book was released on 1960 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient conditions are given for the convergency of a sequence of operators to a given semigroup of non-linear operators in a Banach space, with applications to the approximation of solutions of non-linear partial differential equations by finite-difference methods.
Book Synopsis The Numerical Solution of Ordinary and Partial Differential Equations by : Granville Sewell
Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by John Wiley & Sons. This book was released on 2005-07-25 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn to write programs to solve ordinary and partial differential equations The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations. The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers. The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems. A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students.
Book Synopsis International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics by : Joseph Lasalle
Download or read book International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics written by Joseph Lasalle and published by Elsevier. This book was released on 2012-12-02 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Differential Equations and Nonlinear Mechanics provides information pertinent to nonlinear differential equations, nonlinear mechanics, control theory, and other related topics. This book discusses the properties of solutions of equations in standard form in the infinite time interval. Organized into 49 chapters, this book starts with an overview of the characteristic types of differential equation systems with small parameters. This text then explains the structurally stable fields on a differentiable two manifold are the ones that exhibit the simplest features. Other chapters explore the canonic system of hyperbolic partial differential equations with fixed characteristics. This book discusses as well the monofrequent oscillations that are predominantly near one or the other of the linear modes of motion. The final chapter deals with the existence and asymptotic character of solutions of the nonlinear boundary value problem. This book is a valuable resource for pure and applied mathematicians. Aircraft engineers will also find this book useful.
Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Book Synopsis Numerical Methods for Evolutionary Differential Equations by : Uri M. Ascher
Download or read book Numerical Methods for Evolutionary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 2008-01-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.
Book Synopsis AFOSR. by : United States. Air Force. Office of Scientific Research
Download or read book AFOSR. written by United States. Air Force. Office of Scientific Research and published by . This book was released on 1968 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Book Synopsis Programming for Computations - Python by : Svein Linge
Download or read book Programming for Computations - Python written by Svein Linge and published by Springer. This book was released on 2016-07-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
Book Synopsis Modern Numerical Methods for Ordinary Differential Equations by : G. Hall
Download or read book Modern Numerical Methods for Ordinary Differential Equations written by G. Hall and published by Oxford University Press, USA. This book was released on 1976 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 700 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.
Book Synopsis Programming for Computations - Python by : Svein Linge
Download or read book Programming for Computations - Python written by Svein Linge and published by Springer Nature. This book was released on 2019-10-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.
Book Synopsis On Some Questions Arising in the Approximate Solution of Nonlinear Differential Equations by : Richard Bellman
Download or read book On Some Questions Arising in the Approximate Solution of Nonlinear Differential Equations written by Richard Bellman and published by . This book was released on 1962 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the approximate solution of nonlinear differential equations is explored. The basic idea is to rewrite the nonlinear equations in the form of an infinite sequence of coupled linear equations by application of the Carleman linearization process. The sequence is truncated at a finite stage by a linear closure approximation involving the minimization of the mean square error. Attention is given to the stability of the truncated sequence of linear equations with respect to propagation of error due to closure back to the earlier members of the sequence. The use of suitably defined orthogonal polynomials to simplify closure approximations is considered. The generalization of the general method to the multidimensional case is treated. Consideration is given to the concept of self-consistent closure methods in which the averaging of the squared closure error depends upon the approximate linear equations derived thereby. (Author).
