Improved error estimates for an exponentially convergent quadratures
نویسندگان
چکیده
منابع مشابه
Error estimates for Gauss–Turán quadratures and their Kronrod extensions
We study the kernel Kn,s(z) of the remainder term Rn,s( f ) of Gauss–Turán–Kronrod quadrature rules with respect to one of the generalized Chebyshev weight functions for analytic functions. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L∞-error bounds of Gauss–Turán–Kronrod quadratures. Following Kronrod,...
متن کاملSemiclassical Dynamics with Exponentially Small Error Estimates
We construct approximate solutions to the time–dependent Schrödinger equation i h̄ ∂ψ ∂t = − h̄ 2 2 ∆ψ + V ψ for small values of h̄. If V satisfies appropriate analyticity and growth hypotheses and |t| ≤ T , these solutions agree with exact solutions up to errors whose norms are bounded by C exp {− γ/h̄ } , for some C and γ > 0. Under more restrictive hypotheses, we prove that for sufficiently smal...
متن کاملExponentially convergent lattice sums.
For any oblique incidence and arbitrarily high order, lattice sums for one-dimensional gratings can be expressed in terms of exponentially convergent series. The scattering Green's function can be efficiently evaluated also in the grating plane. Numerical implementation of the method is 200 times faster than for the previous best result.
متن کاملThe Exponentially Convergent Trapezoidal Rule
It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special funct...
متن کاملImproved Estimates of Kinematic Wave Parameters for Circular Channels
The momentum equation in the kinematic wave model is a power-law equation with two parameters. These parameters, which relate the discharge to the flow area, are commonly derived using Manning’s equation. In general, the values of these parameters depend on the flow depth except for some special cross sections. In this paper, improved estimates of the kinematic wave parameters for circular chan...
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: Keldysh Institute Preprints
سال: 2021
ISSN: 2071-2898,2071-2901
DOI: 10.20948/prepr-2021-8