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Author : Simeon Ola Fatunla
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (31 download)
Download or read book Numerical Integrators for Stiff and Highly Oscillatory Differential Equations written by Simeon Ola Fatunla and published by . This book was released on 1977 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Simeon Ola Fatunla
Publisher : Academic Press
ISBN 13 : 1483269264
Total Pages : 308 pages
Book Rating : 4.4/5 (832 download)
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.
Author : Xinyuan Wu
Publisher : Springer Science & Business Media
ISBN 13 : 364235338X
Total Pages : 244 pages
Book Rating : 4.6/5 (423 download)
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.
Author : Linda Ruth Petzold
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (31 download)
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:
Author : Xinyuan Wu
Publisher : Springer
ISBN 13 : 3662481561
Total Pages : 305 pages
Book Rating : 4.6/5 (624 download)
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.
Author : J. Yen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Numerical integration methods for stiff ordinary differential equations in multibody mechanical dynamics written by J. Yen and published by . This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bjorn Engquist
Publisher : Cambridge University Press
ISBN 13 : 0521134439
Total Pages : 254 pages
Book Rating : 4.5/5 (211 download)
Download or read book Highly Oscillatory Problems written by Bjorn Engquist and published by Cambridge University Press. This book was released on 2009-07-02 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.
Author : Xinyuan Wu
Publisher : Springer
ISBN 13 : 9811090041
Total Pages : 356 pages
Book Rating : 4.8/5 (11 download)
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.
Author : J. Hinze
Publisher : Springer
ISBN 13 : 3540393749
Total Pages : 423 pages
Book Rating : 4.5/5 (43 download)
Download or read book Numerical Integration of Differential Equations and Large Linear Systems written by J. Hinze and published by Springer. This book was released on 2006-11-15 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Willard L. Miranker
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Computational Theory of Stiff Differential Equations written by Willard L. Miranker and published by . This book was released on 1976 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Werner Liniger
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (824 download)
Download or read book Optimization of a numerical integration method for stiff systems of ordinary differential equations written by Werner Liniger and published by . This book was released on 1968 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kyle A. Gallivan
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (31 download)
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:
Author : Arieh Iserles
Publisher : Cambridge University Press
ISBN 13 : 9780521410267
Total Pages : 418 pages
Book Rating : 4.4/5 (12 download)
Download or read book Acta Numerica 1992: Volume 1 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1992-04-24 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual volume presenting survey papers in numerical analysis. Each year the editorial board selects significant topics and invites papers from authors who have made notable contributions to the development of that topic. The articles are intended to summarize the field at a level accessible to graduate students and researchers. Acta Numerica is a valuable tool not only for researchers and professionals wishing to develop their understanding of the subject and follow developments, but also as an advanced teaching aid at colleges and universities. This volume was originally published in 1992.
Author : A. Iserles
Publisher : Cambridge University Press
ISBN 13 : 0521734908
Total Pages : 481 pages
Book Rating : 4.5/5 (217 download)
Download or read book A First Course in the Numerical Analysis of Differential Equations written by A. Iserles and published by Cambridge University Press. This book was released on 2009 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.
Author :
Publisher :
ISBN 13 :
Total Pages : 836 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Harvard Lomax
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (31 download)
Download or read book A Critical Analysis of Various Numerical Integration Methods for Computing the Flow of a Gas in Chemical Nonequilibrium written by Harvard Lomax and published by . This book was released on 1967 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alfredo Deano
Publisher : SIAM
ISBN 13 : 1611975115
Total Pages : 207 pages
Book Rating : 4.6/5 (119 download)
Download or read book Computing Highly Oscillatory Integrals written by Alfredo Deano and published by SIAM. This book was released on 2017-12-27 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety. The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals?Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox?from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis?yet this understanding is the cornerstone of efficient algorithms. The text is intended for advanced undergraduate and graduate students, as well as applied mathematicians, scientists, and engineers who encounter highly oscillatory integrals as a critical difficulty in their computations.
