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Sunday, May 10, 2020 | History

2 edition of Numerical methods for integrating oscillatory functions. found in the catalog.

Numerical methods for integrating oscillatory functions.

M. Newby

# Numerical methods for integrating oscillatory functions.

## by M. Newby

Written in English

Edition Notes

M.Sc. dissertation. Typescript.

The Physical Object ID Numbers Series Dissertations Pagination 121p. Number of Pages 121 Open Library OL13693946M

NIntegrate symbolically analyzes its input to transform oscillatory and other integrands, subdivide piecewise functions, and select optimal algorithms. The method suboption "SymbolicProcessing" specifies the maximum number of seconds for which to attempt performing symbolic analysis of . Numerical experiments are carried out for the algorithms discussed in Section 3 and Section 4 for linear hyperbolic equations with oscillatory coefficients and oscillatory initial values. In the numerical experiments, we take the time step size At equal to the space grid size h (the CFL condition is satisfied) and always com-Cited by: 6.

An introduction to highly oscillatory problemsThe wonderful world of asymptotic expansionsOscillatory integrals Design goal of hybrid numerical-asymptotic methods Say f (n) is the solution to Lf = 0. Say Q[f ] is the numerical solution to the approximate equation L hf = 0. Then if f (n) ˘ X1 k=1 a kn k; n ˛1 and g(n) ˘ X1 k=1 b kn k; n ˛1. formula (DIFSUB) of Gear ,  and the blended linear multistep methods of Skeel and Kong , and the symmetric multistep methods of Lambert and Watson . 1. Introduction. The development of numerical integration formulas for stiff as well as highly oscillatory systems of differential equations has attracted considerable.

How to integrate a highly oscillatory function. Follow 16 views (last 30 days) Mila Z on 22 Nov Vote. 0 ⋮ You can't prove divergence of this integral using numerical methods. Try analytical methods instead (e.g. show that the function behaves like constant*cos(2*y) for large y). DRAFT: Integration of oscillatory integrals, a computer-algebra approach Richard Fateman Computer Science University of California Berkeley, CA, USA Novem Abstract The numerical integration of oscillatory integrals is an important and well-studied area of mathemat-ical inquiry.

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### Numerical methods for integrating oscillatory functions by M. Newby Download PDF EPUB FB2

Functions Gradimir V. Milovanovic and Marija P. Stani´ ´c Abstract 1 Introduction By a highly–oscillating function we mean one with large number of local maxima and minima over some interval. The computation of integrals of highly–oscillating functions is one of the most important issues in numerical analysis since such inte-File Size: KB.

Numerical methods for integrating oscillatory functions. book specific nonstandard methods for numerical integration of highly oscillating functions, mainly based on some contour integration methods and applications of some kinds of Gaussian quadratures.

NIntegrate of a highly oscillatory integral double exponential oscillatory. Ask Question Asked 3 years, 8 I see the problem from another point of view. Basically, the integral is a Gaussian multiplying a highly oscillatory function (two functions indeed, a Sin and a Cos). Thanks for contributing an answer to Mathematica Stack Exchange.

Abstract. Some specific nonstandard methods for numerical integration of highly oscillating functions, mainly based on some contour integration methods and applications of some kinds of Gaussian quadratures, including complex oscillatory weights, are presented in this by: 5.

Many effective methods have been proposed for the oscillatory integrals in order to overcome the difficulty caused by the high oscillation such as Filon-type methods [10,11,27], Levin methods [15 Author: Sheehan Olver.

4. Buyst and L. Schotsmans,A method of Gaussian type for the numerical integration of oscillating functions, ICC Bull. 3 (), – Google ScholarCited by: A Method for the Numerical Evaluation of Finite Integrals of Oscillatory Functions By I.

Longman 1. Introduction. In two previous publications [1, 2] the author has demon-strated a method, based on Euler's transformation of slowly convergent alternat. The integration of systems containing highly oscillatory functions is a central point in many practical problems in physics, chemistry and engineering.

Highly oscillatory integrals are allegedly difficult to calculate by the standard classic integration formulae when the frequency is significantly larger than the number of quadrature by: Method for numerical integration of difficult oscillatory integral.

Ask Question Asked 7 years, 3 months ago. i.e. integrating g from 0 to 1 should be the same as integrating f from 0 to $\infty$. Levin-type methods are the best established methods for these kinds of problems. The term "numerical integration" first appears in in the publication A Course in Interpolation and Numeric Integration for the Mathematical Laboratory by David Gibb.

Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean. A Comparison of Some Methods for the Evaluation of Highly Oscillatory Integrals (by G.A.

Evans and r) describes the weighted Clenshaw-Curtis approach to oscillatory integrals. Numerical Approximation of Highly Oscillatory Integrals (PDF) by Sheehan Olver. Read “Lecture 37” in the textbook Numerical Linear Algebra.

satisfies w'(x) =- A(x)w(x) with A(x) an m x m matrix of non-rapidly oscillatory functions, m = kl. Numerical examples In this section we demonstrate the application of the collocation method to three type of oscillatory functions. The first is the well-studied case S(x) = Jv(rx), also treated in [].

TheFile Size: KB. !is an oscillatory kernel which satis es a di erential equation. The aim of this thesis is the numerical approximation of such oscillatory integrals. Perhaps surprisingly, high oscillations make numerical quadrature easier: we will develop methods which actually File Size: 3MB.

Free Online Library: Integrating oscillatory functions in Matlab, II.(Report) by "Electronic Transactions on Numerical Analysis"; Computers and Internet Mathematics Approximation Research Approximation theory Functional equations Functions Functions (Mathematics) Mathematical optimization Optimization theory.

Integrate a Highly Oscillating Function Use hybrid symbolic-numeric methods to immediately solve problem 1 of the SIAM challenge problems, a difficult, highly. other function by a polynomial, and use the fruits of the formula for numerical approximation.

It appears that Mathematica version includes numerical methods for oscillatory integrands including trigonometric and Bessel functions, though the methods are not speci ed. New Runge–Kutta methods specially adapted to the numerical integration of IVPs with oscillatory solutions are obtained.

The coefficients of these methods are frequency-dependent such that certain particular oscillatory solutions are computed exactly (without truncation errors).Cited by: In this paper we give a short account of the most important methods for the evalua-tion of integrals of oscillatory functions (Sections 2 and 3), and an uniﬁed approach for such a purpose in Section 4.

FILON’S RULE, GAUSSIANFORMULAE ANDINTEGRATION BETWEEN ZEROS The earliest formulas for numerical integration of rapidly oscillatory.

Stack Exchange network consists of Q&A communities including Stack Overflow, Numerical intergration of a complex, oscillatory function (Bessel function, Singularities) Ask Question Browse other questions tagged numerical-methods bessel-functions. 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 numerical analysis. In this work we developed efficient numerical algorithms for solving highly oscillatory differential equations.

The main important achievements are: to the contrary of classical Author: Marianna Khanamiryan. on haar wavelets and hybrid functions, Comput Math Applpp.

–  Siraj-ul-Islam,Aziz, I, KhanW, Numerical integration of multi-dimensional highly oscillatory, gentle oscillatory and non-oscillatory integrands based on wavelets and radial basis functions, Engineering Analysis with Boundary Elements,pp.

–pose of the research is to nd appropriate integration methods for the oscillatory integrals, we made use of di erent in-built Mathematica functions. We calculated the oscillatory integrals by the use of those various functions.

We then compared the result from di erent integration methods to choose the best method that does the calculation faster.This book provides an up-to-date overview of methods for computing special functions and discusses when to use them in standard parameter domains, as well as in large and complex domains.

The first part of the book covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations.