ISSN:
0029-5981
Keywords:
convergence
;
finite-part (hypersingular) integrals
;
numerical integration
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The method of finite-part (Hadamard-type or hypersingular) integrals is already a standard approach in applied numerical methods in engineering and, mainly, in acoustics, fluid dynamics, elasticity and fracture mechanics. Here we study the convergence of the non-classical (possessing a negative node, outside the integration interval, as well as a negative weight corresponding to this node) Gauss-Legendre quadrature rule for finite-part integrals on the interval [0,1] with the weight function 1/y and we prove its validity for integrands possessing a continuous first derivative. The case of integrands possessing a higher-order derivative is also considered and the rate of convergence is established. These results are based on the derivation of a bound for the negative node in the above quadrature rule and, further, on the theory of convergence of the classical Gauss quadrature rule. Numerical results, verifying the results of this paper, are also displayed. The present results can be generalized to the Gauss-Laguerre similarly non-classical quadrature rule for finite-part integrals (on the interval [0], ∞)) as well as to the two special, but important in engineering applications, non-classical Gaussian quadrature rules for Cauchy-type principal-value integrals and Mangler-type finite-part integrals have been proposed by Tsamasphyros and Dimou.
Additional Material:
2 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620381408
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