scholarly journals Computation of Hyperspherical Bessel Functions

2017 ◽  
Vol 22 (3) ◽  
pp. 852-862 ◽  
Author(s):  
Thomas Tram
Keyword(s):  
Numerical Algorithm ◽  
Bessel Functions ◽  
Gegenbauer Polynomials ◽  
Stable Algorithm ◽  
Large Order ◽  
Closed Type ◽  
Accurate Numerical Algorithm

AbstractIn this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapper is available upon request.

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

2012 ◽  
Vol 67 (12) ◽  
pp. 665-673 ◽  
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya ◽  
Jamal Amani Rad ◽  
Fatemeh Baharifard
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Nonlinear Ordinary Differential Equation ◽  
Finite Domain ◽  
Algebraic Equations ◽  
Infinite Domain ◽  
Third Order ◽  
Domain Truncation

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

An accurate numerical algorithm for solving compressible three-phase flows in porous media

1997 ◽  
Vol 66 (1-2) ◽  
pp. 57-88 ◽  
Author(s):  
Mazen Saad ◽  
J.B. Bell ◽  
J.A. Trangenstein ◽  
G.R. Schubin ◽  
A. Harten ◽  
...  
Keyword(s):  
Porous Media ◽  
Numerical Algorithm ◽  
Flows In Porous Media ◽  
Three Phase ◽  
Accurate Numerical Algorithm

scholarly journals The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions

2014 ◽  
Vol 12 (04) ◽  
pp. 403-462 ◽  
Author(s):  
Gergő Nemes
Keyword(s):  
Error Bounds ◽  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Smooth Transition ◽  
Large Order ◽  
Computable Error Bounds

The aim of this paper is to derive new representations for the Hankel and Bessel functions, exploiting the reformulation of the method of steepest descents by Berry and Howls [Hyperasymptotics for integrals with saddles, Proc. R. Soc. Lond. A 434 (1991) 657–675]. Using these representations, we obtain a number of properties of the large-order asymptotic expansions of the Hankel and Bessel functions due to Debye, including explicit and numerically computable error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.

scholarly journals An Accurate Numerical Algorithm for Attitude Updating Based on High-Order Polynomial Iteration

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 95892-95902 ◽  
Author(s):  
Xixiang Liu ◽  
Xiaole Guo ◽  
Wenqiang Yang ◽  
Yixiao Wang ◽  
Wei Chen ◽  
...  
Keyword(s):  
Numerical Algorithm ◽  
High Order ◽  
Order Polynomial ◽  
Accurate Numerical Algorithm

The asymptotic expansion of bessel functions of large order

1954 ◽  
Vol 247 (930) ◽  
pp. 328-368 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Bessel Functions ◽  
Airy Functions ◽  
Elementary Functions ◽  
Large Order ◽  
Hankel Functions ◽  
Rapid Calculation ◽  
Zeros Of Functions ◽  
Significant Figures ◽  
Complex Zeros

New expansions are obtained for the functions Iv{yz), ) and their derivatives in terms of elementary functions, and for the functions J v(vz), Yv{vz), H fvz) and their derivatives in terms of Airy functions, which are uniformly valid with respect to z when | | is large. New series for the zeros and associated values are derived by reversion and used to determine the distribution of the zeros of functions of large order in the z-plane. Particular attention is paid to the complex zeros of 7„(z) and the Hankel functions when the order n is an integer or half an odd integer, and for this purpose some new asymptotic expansions of the Airy functions are derived. Tables are given of complex zeros of Airy functions and other quantities which facilitate the rapid calculation of the smaller complex zeros of 7„(z), 7'(z), and the Hankel functions and their derivatives, when 2 n is an integer, to an accuracy of three or four significant figures.

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