Download or read book Asymptotic Integration Algorithms for Nonhomogeneous Nonlinear First Order Ordinary Differential Equations written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-11 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist. Walker, K. P. and Freed, A. D. Glenn Research Center RTOP 553-13-00...
Download or read book Asymptotic Integration Algorithms for Nonhomogeneous Nonlinear First Order Ordinary Differential Equations written by and published by . This book was released on 1991 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Asymptotic Integration Algorithms for One dimensional Autonomous Dissipative First order ODEs written by and published by . This book was released on 1994 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotics for Dissipative Nonlinear Equations written by Nakao Hayashi and published by Springer Science & Business Media. This book was released on 2006-04-21 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Download or read book Asymptotic Analysis of Differential Equations written by R. B. White and published by World Scientific. This book was released on 2010 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Download or read book NASA Tech Briefs written by and published by . This book was released on 1994 with total page 348 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 1994 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Asymptotic Solution of the Non homogeneous Linear Differential Equation of the N th Order written by William Van Nest Garretson and published by . This book was released on 1918 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Analysis written by Mikhail Vasilʹevich Fedori︠u︡k and published by Springer. This book was released on 1993 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Solutions of Differential Equations and Their Applications written by Calvin Hayden Wilcox and published by . This book was released on 1964 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations written by and published by . This book was released on 1989 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Asymptotic Analysis written by Mikhail V Fedoryuk and published by . This book was released on 1993-05-03 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Download or read book Asymptotic Behavior of Solutions and Adjunction Fields for Nonlinear First Order Differential Equations written by Walter Charles Strodt and published by . This book was released on 1971 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Theory of Second order Nonlinear Ordinary Differential Equations written by Bita Jenab and published by . This book was released on 1985 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
