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Detection And Integration Of Oscillatory Differential Equations With Initial Stepsize Order And Method Selection
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Book Synopsis Detection and Integration of Oscillatory Differential Equations with Initial Stepsize, Order and Method Selection by : Kyle A. Gallivan
Download or read book Detection and Integration of Oscillatory Differential Equations with Initial Stepsize, Order and Method Selection written by Kyle A. Gallivan and published by . This book was released on 1980 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Detection and Integration of Oscillatory Differential Equations with Initial Stepsize, Order and Method Selection by :
Download or read book Detection and Integration of Oscillatory Differential Equations with Initial Stepsize, Order and Method Selection written by and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Within any general class of problems there typically exist subclasses possessed of characteristics that can be exploited to create techniques more efficient than general methods applied to these subclasses. Two such subclasses of initial-value problems in ordinary differential equations are stiff and oscillatory problems. Indeed, the subclass of oscillatory problems can be further refined into stiff and nonstiff oscillatory problems. This refinement is discussed in detail. The problem of developing a method of detection for nonstiff and stiff oscillatory behavior in initial-value problems is addressed. For this method of detection a control structure is proposed upon which a production code could be based. An experimental code using this control structure is described, and results of numerical tests are presented. 3 figures.
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 1989 with total page 956 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1981 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Masters Theses in the Pure and Applied Sciences by : Wade Shafer
Download or read book Masters Theses in the Pure and Applied Sciences written by Wade Shafer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Masters Theses in the Pure and Applied Sciences was first conceived, published, and disseminated by the Center for Information and Numerical Data Analysis and Synthesis (CINDAS) * at Purdue University in 1957, starting its coverage of theses with the academic year 1955. Beginning with Volume 13, the printing and dissemination phases of the activity were transferred to University Microfilms/Xerox of Ann Arbor, Michigan, with the thought that such an arrangement would be more beneficial to the academic and general scientific and technical community. After five years of this joint undertaking we had concluded that it was in the interest of all con cerned if the printing and distribution of the volume were handled by an international publishing house to assure improved service and broader dissemination. Hence, starting with Volume 18, Masters Theses in the Pure and Applied Sciences has been disseminated on a worldwide basis by Plenum Publishing Cor poration of New York, and in the same year the coverage was broadened to include Canadian universities. All back issues can also be ordered from Plenum. We have reported in Volume 26 (thesis year 1981) a total of 11 ,048 theses titles from 24 Canadian and 21 8 United States universities. We are sure that this broader base for these titles reported will greatly enhance the value of this important annual reference work. While Volume 26 reports theses submitted in 1981, on occasion, certain univer sities do report theses submitted in previous years but not reported at the time.
Download or read book Numerical Analysis written by G.A. Watson and published by Springer. This book was released on 2006-11-14 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
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.
Book Synopsis Structure-Preserving Algorithms for Oscillatory Differential Equations by : Xinyuan Wu
Download or read book Structure-Preserving Algorithms for Oscillatory Differential Equations written by Xinyuan Wu and published by Springer Science & Business Media. This book was released on 2013-02-02 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations. The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.
Book Synopsis Structure-Preserving Algorithms for Oscillatory Differential Equations II by : Xinyuan Wu
Download or read book Structure-Preserving Algorithms for Oscillatory Differential Equations II written by Xinyuan Wu and published by Springer. This book was released on 2016-03-03 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods. The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and scientists investigating oscillatory systems, as well as for teachers and students who are interested in structure-preserving algorithms for differential equations.
Book Synopsis Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations by : Xinyuan Wu
Download or read book Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations written by Xinyuan Wu and published by Springer. This book was released on 2018-04-19 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.
Book Synopsis Method and Initial Stepsize Selection in Multistep ODE Solvers by : Charles William Gear
Download or read book Method and Initial Stepsize Selection in Multistep ODE Solvers written by Charles William Gear and published by . This book was released on 1980 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Initial Value Problems in Ordinary Differential Equations by : Simeon Ola Fatunla
Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by Academic Press. This book was released on 2014-05-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.
Book Synopsis Publications of the State of Illinois by :
Download or read book Publications of the State of Illinois written by and published by . This book was released on 1983 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations by : Linda Ruth Petzold
Download or read book An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations written by Linda Ruth Petzold and published by . This book was released on 1978 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Automatic Detection and Treatment of Oscillatory And/or Stiff Ordinary Differential Equations by : Charles William Gear
Download or read book Automatic Detection and Treatment of Oscillatory And/or Stiff Ordinary Differential Equations written by Charles William Gear and published by . This book was released on 1980 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Automatic Detection and Treatment of Oscillatory And/or Stiff Ordinary Differential Equations by :
Download or read book Automatic Detection and Treatment of Oscillatory And/or Stiff Ordinary Differential Equations written by and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The next generation of ODE software can be expected to detect special problems and to adapt to their needs. The low-cost, automatic detection of oscillatory behavior, the determination of its period, and methods for its subsequent efficient integration are addressed here, along with stiffness detection. In the first phase, the method for oscillatory problems discussed examines the output of any integrator to determine if the output is nearly periodic. At the point this answer is positive, the second phase is entered and an automatic, nonstiff, multirevolutionary method is invoked. This requires the occasional solution of a nearly periodic initial-value problem over one period by a standard method and the re-determination of its period. Because the multirevolutionary method uses a very large step, the problem has a high probability of being stiff in this second phase. Hence, it is important to detect if stiffness is present so that an appropriate stiff, multirevolutionary method can be selected. 6 figures.
Book Synopsis Stiff Computation by : Richard C. Aiken
Download or read book Stiff Computation written by Richard C. Aiken and published by Oxford University Press, USA. This book was released on 1985 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
