The superconvergence of the Newton–Cotes rule for Cauchy principal value integrals
نویسندگان
چکیده
منابع مشابه
A Sinc-hunter Quadrature Rule for Cauchy Principal Value Integrals
A Sine function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval (-1, 1). It is shown that the quadrature error is of order 0(e~ ), where N is the number of nodes used, and w...
متن کاملOn the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals*
The authors give convergence theorems for interpolatory product rules for evaluating Cauchy singular integrals and obtain asymptotic estimates of the remainder. Some results, previously established by other authors, are generalized and improved.
متن کاملTWO LOW-ORDER METHODS FOR THE NUMERICAL EVALUATION OF CAUCHY PRINCIPAL VSlLUE INTEGRALS OF OSCILLATORY KIND
In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...
متن کاملGeneralized Noninterpolatory Rules for Cauchy Principal Value Integrals
Consider the Cauchy principal value integral I(kf;X)=i k{x)F^Ldx, -1<A<1. 7-1 x — A If we approximate f(x) by Yli=oajP¡(x'i w) where {p } is a sequence of orthonormal polynomials with respect to an admissible weight function w and û, = (/. P.), then an approximation to I(kf; X) is given by X!/=o ajl(kp¡ ; ^)If, in turn, we approximate a¡ by ajm = £TM , wimf(x¡m)Pj(xim), then we get a double seq...
متن کاملGauss-Kronrod Integration Rules for Cauchy Principal Value Integrals
Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod extension involves evaluating the derivative of the integrand, a new extension is introduced using n + 2 points which requires only values of the integrand. However, this new rule does not exist for all n...
متن کاملذخیره 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: Journal of Computational and Applied Mathematics
سال: 2010
ISSN: 0377-0427
DOI: 10.1016/j.cam.2010.06.023