On the Convergence Problem of One-Dimensional Hypersingular Integral Equations

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Approximations of hypersingular integral equations by the quadrature method

A numerical method is proposed and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities. The proposed approximation method is an extension beyond the quadrature method. Moreover an error estimates theory is introduced for the hypersingula...

متن کامل

Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method

Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved to be convergent. Then, Tranter’s method is discussed. This method was devised in the 1950s to solve certain pairs of dual integral equations. It is shown that this method is a...

متن کامل

Hypersingular Integral Equations in Banach Spaces by the Quadrature Method

Abstract A new numerical method is introduced and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities.The proposed approximation method is an extension beyond the quadrature method. Beyond the above, an error estimates theory is proposed...

متن کامل

Convergence of Integral Functionals of One-dimensional Diffusions

In this paper we describe the pathwise behaviour of the integral functional ∫ t 0 f(Yu) du for any t ∈ [0, ζ], where ζ is (a possibly infinite) exit time of a one-dimensional diffusion process Y from its state space, f is a nonnegative Borel measurable function and the coefficients of the SDE solved by Y are only required to satisfy weak local integrability conditions. Two proofs of the determi...

متن کامل

Compact Numerical Quadrature Formulas for Hypersingular Integrals and Integral Equations

In the first part of this work, we derive compact numerical quadrature formulas for finite-range integrals I [f ] = ∫ b a f (x) dx, where f (x)= g(x)|x − t |β , β being real. Depending on the value of β, these integrals are defined either in the regular sense or in the sense of Hadamard finite part. Assuming that g ∈ C∞[a, b], or g ∈ C∞(a, b) but can have arbitrary algebraic singularities at x ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematical Problems in Engineering

سال: 2013

ISSN: 1024-123X,1563-5147

DOI: 10.1155/2013/974751