4,392 research outputs found
Lubich convolution quadratures and their application to problems described by space-time BIEs
No full textA note on extended Gaussian quadrature rules
No full textExtended Gaussian quadrature rules of the type first considered by Kronrod are examined. For a general nonnegative weight function, simple formulas for the computation of the weights are given, together with a condition for the positivity of the weights associated with the new nodes. Examples of nonexistence of these rules are exhibited for the weight functions
(
1
−
x
2
)
λ
−
1
/
2
(1-x^2)^{\lambda - 1/2}
,
e
−
x
2
e^{-x^2}
and
e
−
x
e^{-x}
. Finally, two examples are given of quadrature rules which can be extended repeatedly.</p
The numerical evaluation of a 2D Cauchy principal value integral arising in boundary integral equation methods
No full textIn this paper we consider the problem of computing 2-D Cauchy principal value integrals of the form
₯
S
F
(
P
0
;
P
)
d
P
,
P
0
∈
S
,
{\fint _S}F({P_0};P)\,dP,\qquad {P_0} \in S,
where S is either a rectangle or a triangle, and
F
(
P
0
;
P
)
F({P_0};P)
is integrable over S, except at the point
P
0
{P_0}
where it has a second-order pole. Using polar coordinates, the integral is first reduced to the form
where
[
u
n
k
]
[unk]
denotes the finite part of the (divergent) integral. Then ad hoc products of one-dimensional quadrature rules of Gaussian type are constructed, and corresponding convergence results derived. Some numerical tests are also presented.</p
Some remarks on the construction of extended Gaussian quadrature rules
No full textWe recall some results from a paper by Szegö on a class of polynomials which are related to extended Gaussian quadrature rules. We show that a very efficient algorithm, for the computation of the abscissas of the rules in question, was already described in that paper. We also point out that this method extends to rules for integrals with an ultraspherical-type weight function. A bound for the error of some of the above rules is also given.</p
Some new problems in numerical integration
No full textAbstractIn this paper, we examine the numerical computation of the (multiple) integrals generated by Galerkin methods applied to two nonstandard hypersingular integral equations, which are of interest by their own. These equations are used to solve two classical electromagnetic problems that are briefly described
On a time discrete convolution - space collocation BEM for the numerical solution of 2D wave propagation problems in unbounded domains
No full text
On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives
No full text- …
