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On the uniform approximation of a class of singular integral equations in a Hölder space

A. W. McInnes

On the uniform approximation of a class of singular integral equations in a Hölder space

by A. W. McInnes

  • 34 Want to read
  • 25 Currently reading

Published .
Written in English

    Subjects:
  • Numerical solutions,
  • Integral equations,
  • Approximation theory,
  • Linear topological spaces,
  • Numerical integration

  • Edition Notes

    Statementby Allan William McInnes
    The Physical Object
    Paginationiv, 115 leaves, bound ;
    Number of Pages115
    ID Numbers
    Open LibraryOL25450507M
    OCLC/WorldCa173224384

      Cauchy kernel are important in many fields of applied mathematics. The method can be developed and applied to other class of integral and integro-differential equations. The advantage of this method is that we can eliminate the singularity, and compute an approximate solution through a system of linear equations.   In this paper we propose new numerical methods for linear Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations.

    New preprints and reprints in pdf format: () A. Cialdea, V. Maz'ya, Criterion for the functional dissipativity of second order differential operators with() F. Lanzara, V. Maz'ya, G. Schmidt, Fast computation of elastic and hydrodynamic potentials using approximate approximations() G. Kresin, V. Maz'ya, Sharp pointwise estimates for solutions of weakly coupled second order parabolic. good numerical approximations for a large class of singular integral equations on the line. The exact form of the equations studied is motivated, in part, by concr ete applications (see [1, 2, 12, 13] and the references cited therein), and so is of current interest and importance.

    This paper aims to present a Clenshaw–Curtis–Filon quadrature to approximate thesolution of various cases of Cauchy-type singular integral equations (CSIEs) of the second kind witha highly oscillatory kernel function. We adduce that the zero case oscillation (k = 0) proposed methodgives more accurate results than the scheme introduced in Dezhbord at el. () and Eshkuvatovat el. (   Free Online Library: Fast Solvers of Weakly Singular Integral Equations of the Second Kind.(Report) by "Mathematical Modeling and Analysis"; Mathematics Coefficients Measurement Derivatives (Mathematics) Research Integral equations Kernel functions Mathematical research Singularities (Mathematics).


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On the uniform approximation of a class of singular integral equations in a Hölder space by A. W. McInnes Download PDF EPUB FB2

Alexander G. Kyurkchan, Nadezhda I. Smirnova, in Mathematical Modeling in Diffraction Theory, Derivation of CBCM Integral Equations. The CBCM integral equations are obtained according to the same scheme as the singular integral definiteness, we assume that the boundary S is piecewise smooth.

As S δ we take a piecewise smooth surface containing S and lying at a. The Theory of Approximate Methods and Their Application to the Numerical Solution of Singular Integral Equations, Translated by A.

Ideh, translation edited by R. Anderssen and D. Elliott, Noordhoff International Publishing Company, Leyden, Holland, (Russian edition published in ).Cited by:   This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values.

Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problems, the Dirichlet problem, inversion formulas for arcs, and many other by: The paper is devoted to the foundation of approximation methods for integral equations of the form (aI+SbI+K)f=g, where S is the Cauchy singular integral operator on (-1,1) and K is a weakly.

Request PDF | On Jun 8,Madan Mohan Panja and others published Wavelet Based Approximation Schemes for Singular Integral Equations | Find, read and cite all the research you need on ResearchGate.

In this paper the method of Kantorovich majorants[7,18,20], has been applied to the following class of nonlinear singular integral equations with Hilbert kernel. Weighted Besov spaces are introduced and used as a powerful tool in studying the uniform convergence of polynomial approximation methods for Cauchy singular integral equations in [6].

Abstract. We establish the uniform convergence of a collocation method for solving a class of singular integral equations. This method uses the Jacobi polynomials {P n (α, β)} as basis elements and the zeros of a Chebyshev polynomial of the first kind as collocation m convergence is shown to hold under the weak assumption that the kernel and the right-hand side are Hölder.

In this paper we propose numerical treatment for singular integral equations. The methods are developed by means of the Sinc approximation with smoothing transformations. Such approximation is an effective technique against the singularities of the equations, and achieves exponential convergence.

McInnes,On the Uniform Approximation of a Class of Singular Integral Equations in a Hölder Space, Ph.D. thesis at the University of Illinois, Urbana-Champaign (). [22] G. Szegö, Orthogonal Polynomials, revised edition, American Math.

Soc. integral equations. Thus, we develop the test conditions for the convergence of convolution type singular integral operators to approximated function in the exponential weighted space.

An application for the Gauss-Weierstrass integral is given. Key-Words: Convolution operators, The order of approximation, the weighted modulus of continuity. singular equations more economical. We also note the extensive treatment in Baker's book [4, Sections ], where the performance of most of the standard methods, as applied to the numerical solution of weakly singular equations is discussed.

Many numerical examples are given there, and also in the reports of Bechlars [5] and Volk [33]. Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory.

They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics. The Newton-Kantorovich Approximations for Nonlinear Singular Integral Equations with Shift Article in Journal of Integral Equations and Applications 14(3) September with 10 Reads.

of a continuous vector solution y = y(t) to the integral equation y(t) = u(t) + EL(t) Ef t M(s) f(s,y(s)) ds + K(t,s) f(s,y(s)) ds, t 0 are derived.

A successive approximation technique involving a double sequence is used in the proof. This integral equation result is applied to the second order singular.

A certain type of singular integral operator which has played an important role in the historical development of the theory of elliptic PDEs is the so-called layer potential, see for example [21] for a very classical potentials actually come in two common varieties.

If Γ denotes the fundamental solution () of Laplace’s equation in R N for N ≥ 2, and Σ ⊂ R N is a. MT - Integral equations Introduction Integral equations occur in a variety of applications, often being obtained from a differential equation.

The reason for doing this is that it may make solution of the problem easier or, sometimes, enable us to prove fundamental results on. A comprehensive approach to the approximate solution of singular integral equations: David Elliott: 2: 1: Winter /JIE Projection methods for singular integral equations: David Elliott: 2: 1: Winter /JIE Discrete numerical solvability of Hammerstein integral equations of mixed type: M.

Ganesh. Gakhov F D and Chibrikova L I On some types of singular integral equations that can be solved in a closed form Mat. 35 [25] Gakhov F D On the present state of the boundary value theory of analytic functions and the theory of singular integral equations (Proc.

of the Seminar on boundary value problems), no. 7 (Izd. This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy.

equations contain one or more free parameters (the book actually deals with families of integral equations); it is the reader’s option to fix these parameters. Totally, the number of equations described in this handbook is an order of magnitude greater than in any other book currently available.() Approximations of singular integral equations on Lyapunov contours in Banach spaces.

Computers & Mathematics with Applications() Recovering a compactly supported function from knowledge of its Hilbert transform on a finite interval.1. INTRODUCTION The system of singular integral equations of the form 1M may be found in the formulation of many boundary value problems containing geometric singularities.

In (l), the functions aij, bij the kernels kij are also known and satisfy a Holder condition in each of the variables t and T, and the unknown functions oi are likewise required to satisfy a Holder condition.