Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0614.65012
Bezvoda, Václav; Farzan, Ruszlán; Segeth, Karel; Takó, Galina
On numerical evaluation of integrals involving Bessel functions. (English)
[J] Apl. Mat. 31, 396-410 (1986). ISSN 0373-6725

The authors discuss the numerical computation of the integral $$ I=\int\sp{\infty}\sb{0}f(x)J\sb n(rx)\quad dx $$ for fixed integer $n\ge 0$ and a given set of real values of r. In a first approach, they replace the Bessel function $J\sb n(x)$ by a well-known trigonometric integral and then compute I by using a fast Fourier transform procedure. The second method consists of the construction of weights and abscissas for a Gaussian integration formula with $J\sb n(x)$ a weight function over the intervals between two consecutive zeros of $J\sb n(x)$. A comparison shows that the second method, once the weights and abscissas have been obtained, is more efficient. A table of weights and abscissas for a five- point Gauss rule is given and an error analysis is presented. An appropriate application of any of the existing adaptive quadrature procedures is not discussed.
[K.S.Kölbig]

MSC 2000:: *65D20 Computation of special functions
65T40 Trigonometric approximation and interpolation
65D32 Quadrature formulas (numerical methods)
33C10 Cylinder functions, etc.
42A16 Fourier coefficients, etc.

Keywords: integrals with Bessel functions; fast Fourier transform; Gaussian integration formula; five-point Gauss rule; error analysis

Cited in: Zbl 0704.65104 Zbl 0693.65094

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]