相关论文: Computation of highly oscillatory Bessel transform…
A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order $0$ as well as evaluating Schl\"{o}milch and Fourier--Bessel expansions in $\mathcal{O}(N(\log N)^2/\log\!\log N)$ operations. The…
We present an algorithm for the efficient numerical evaluation of integrals of the form \[ I(\omega) = \int_0^1 F( x,\mathrm e^{\mathrm i \omega x}; \omega) \, \mathrm d x \] for sufficiently smooth but otherwise arbitrary $F$ and $\omega…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
We present an efficient self-contained algorithm for computing the modified Bessel function of the first kind $I_{\nu}(z)$, implemented in a robust Fortran code supporting double and quadruple (quad) precision. The algorithm overcomes the…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
In this article, we develop a new method to approximate numerically the fractional Laplacian of functions defined on $\mathbb R$, as well as some more general singular integrals. After mapping $\mathbb R$ into a finite interval, we…
The inversion of cosh-Hilbert transform (CHT) is one of the most crucial steps for single-photon emission computed tomography with uniform attenuation from truncated projection data. Although the uniqueness of the CHT inversion had been…
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$…
In this paper, we investigate the rate of convergence of Clenshaw-Curtis quadrature and its acceleration for functions with endpoint singularities in X^s, where X^s denotes the space of functions whose Chebyshev coefficients decay…
We record what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. More generally, we develop formulae for integrals of…
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor…
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…