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Tuesday, April 21, 2020 | History

1 edition of An efficient numerical method for highly oscillatory ordinary differential equations found in the catalog.

An efficient numerical method for highly oscillatory ordinary differential equations

Linda Ruth Petzold

An efficient numerical method for highly oscillatory ordinary differential equations

  • 369 Want to read
  • 23 Currently reading

Published by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana .
Written in English

    Subjects:
  • Numerical solutions,
  • Initial value problems,
  • Data processing,
  • Eigenvalues

  • Edition Notes

    Statementby Linda Ruth Petzold
    SeriesReport (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no. 933, Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no. 933.
    Classifications
    LC ClassificationsQA76 .I4 no. 933, QA378 .I4 no. 933
    The Physical Object
    Paginationiv, 131 p. :
    Number of Pages131
    ID Numbers
    Open LibraryOL25508567M
    OCLC/WorldCa4280583


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An efficient numerical method for highly oscillatory ordinary differential equations by Linda Ruth Petzold Download PDF EPUB FB2

A “quasi-envelope” of the solution of highly oscillatory differential equations is defined. For many problems this is a smooth function which can be integrated using much larger steps than are Cited by: We present a novel numerical routine (oscode) with a C++ and Python interface for the efficient solution of one-dimensional, second-order, ordinary differential equations with rapidly oscillating solutions.

The method Cited by: 4. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for. An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations An efficient numerical method for highly oscillatory ordinary differential equations book (PDF Available) in SIAM Journal on Numerical Analysis 18(3) June with ReadsAuthor: Linda Petzold.

This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential : Marianna Khanamiryan. Automatic methods for highly oscillatory ordinary differential equations. Abstract.

By a highly oscillatory An efficient numerical method for highly oscillatory ordinary differential equations book we mean one whose solution is “nearly periodic.” This paper is concerned with the low-cost, automatic detection of oscillatory behavior, the determination of its period, and methods for its subsequent efficient by: This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations.

Phenomena of high oscillation is considered. STIFF AND HIGHLY OSCILLATORY DIFFERENTIAL EQUATIONS In this paper, we propose some two-point numerical integration formulas which effectively cope with systems of ODEs whose.

Denk, A new numerical method for the integration of highly oscillatory second order differential equations, Appl. Numer. Math. 13 (), pp. 57– MathSciNet zbMATH CrossRef Google ScholarCited by: 3. Current research made contribution to the numerical analysis of highly oscillatory ordinary differential equations.

Highly oscillatory functions appear to be at the forefront of the research in Author: Marianna Khanamiryan. We present a numerical routine (uc(oscode)) with a C ++ and Python interface for the efficient solution of one-dimensional, second-order, An efficient numerical method for highly oscillatory ordinary differential equations book differential equations with rapidly oscillating solutions.

The method. Gallivan, K. A., An algorithm for the detection and integration of highly oscillatory ordinary differential equations using a generalized unified modified divided difference representation, Dept. Rept. R Cited by: A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject.

The study of numerical methods for solving ordinary differential equations is. on developing numerical methods efficient for solving linear and non-linear systems of highly oscillatory differential equations.

The key problem of our discussion throughout the thesis is a family of highly oscillatory. In this paper, we study efficient numerical integrators for linear and nonlinear systems of highly oscillatory second-order ordinary differential equations.

The systems are reformulated as a first Cited by: 4. Abstract We propose in this paper a novel technique for an efficient numerical approximation of systems of highly oscillatory ordinary differential equations. In particular, we consider electronic.

This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations.

Phenomena of high oscillation is considered a Author: Marianna Khanamiryan. Efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems January DOI: /PhysRevResearch Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book.

A complete self-contained theory of symplectic and symmetric methods. The next generation of ODE software can be expected to detect special problems and to adapt to their needs. This paper is principally concerned with the low-cost, automatic detection of oscillatory behavior, the determination of its period, and methods for its subsequent efficient by: 7.

A new numerical method for the integration of highly oscillatory second-order ordinary differential equations, Applied Numerical Mathematics 13 () This paper presents a new discretization scheme for the efficient integration of highly oscillatory second-order ordinary differential by: Numerical Integrators for Stiff and Highly Oscillatory Differential Equations By Simeon Ola Fatunla* Abstract.

Some L-stable fourth-order explicit one-step numerical integration formulas which require no matrix inversion are proposed to cope effectively with systems of ordinary differential equations. Ordinary differential equations occur in many scientific disciplines, for instance in physics, chemistry, biology, and economics.

In addition, some methods in numerical partial differential equations convert. Introduction. Highly oscillatory problems have appeared in many fields such as celestial mechanics, chemistry, biology, classical and quantum mechanics, and engineering. Due to the oscillatory Author: Zhongli Liu, Tianhai Tian, Hongjiong Tian.

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is.

The subject of this book is numerical methods that preserve geometric properties of. the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for. A new numerical method for the integration of highly oscillatory second-order ordinary differential equations.

of the formulas reveals properties such as absolute stability and P-stability which indicate the ability of the method to handle highly oscillatory differential equations. This is confirmed by numerical Cited by: Petzold was the first winner of the J.

Wilkinson Prize for Numerical Software, for her work on DASSL, a system for the numerical solution of differential algebraic equations.

In she won the SIAM/ACM Alma mater: University of Illinois at Urbana-Champaign. EFFICIENT COMPUTATION OF DELAY DIFFERENTIAL EQUATIONS WITH HIGHLY OSCILLATORY TERMS Marissa Condon1, Alfredo Deano˜ 2, Arieh Iserles3 and Karolina Kropielnicka3,4 Abstract.

This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory. 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 Manufacturer: Springer. In this work we show that our methods introduce better accuracy of approximation as compared with the state of the art solvers in Matlab and thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential : Marianna Khanamiryan.

Purpose – The purpose of this paper is to analyse a novel technique for an efficient numerical approximation of systems of highly oscillatory ordinary differential equations (ODEs) that arise in electronic systems subject to modulated signals.

Design/methodology/approach – The paper combines a Filon‐type method. 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 Cited by: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics (31)) 2nd ed.

2nd printing Edition by Ernst Cited by:   Numerical solution of highly oscillatory ordinary differential equations - Volume 6 - Linda R.

Petzold, Laurent O. Jay, Jeng Yen Efficient numerical integrators for highly oscillatory dynamic systems based on and in differential-algebraic equations (DAEs) is the development of methods for dealing with highly oscillatory Cited by: text, we consider numerical methods for solving ordinary differential equations, that is, those differential equations that have only one independent variable.

The differential equations we consider in most of the book File Size: 1MB. – The purpose of this paper is to analyse a novel technique for an efficient numerical approximation of systems of highly oscillatory ordinary differential equations (ODEs) that arise in electronic systems subject to modulated signals., – The paper combines a Filon‐type method with waveform relaxation techniques for nonlinear systems of ODEs., – The analysis includes numerical Cited by: An efficient new iterative method for oscillator differential equation.

The method overcomes the difficulties that appear in numerical methods because it is efficient. We confirm that one can use this method for any highly nonlinear oscillator differential by:   oscode is a C++ tool with a Python interface that solves oscillatory ordinary differential equations is designed to deal with equations of the form.

where (friction term) and. This paper is concerned with the asymptotic expansion and numerical solu-tion of systems of linear delay differential equations with highly oscillatory forc-ing terms. The computation of such problems using standard numerical methods.

Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential pdf between trigonometric integrators and splitting methods for highly oscillatory differential equations, IMA Journal of Numerical importantly, is it then possible to construct and analyze efficient numerical Cited by: 5.The book concludes with a chapter on the abstract framework of the finite element method for differential equations.

Volume 2, to be published in earlyextends the scope to nonlinear differential equations and systems of equations Cited by: Iterative method. Link to description of algorithm: Jeffareid ebook, 20 July (UTC) That's not about computing integrals but computing the solution of a differential equation; see Numerical ordinary differential equations.(Rated B-class, High-importance): WikiProject .