Truncated quadrature rules over \((0,\infty)\) and Nyström-type methods. (English) Zbl 1056.65022
The authors propose replacing the classical Gauss-Laguerre quadrature formula over an infinite interval, by a truncated version of it, obtained by eliminating the last part of its nodes. An error estimate for this new quadrature is obtained, which includes, as a particular case, the estimate for the error term of the given Gauss-Laguerre quadrature. A similar new error bounds are obtained for corresponding product-type rules, having a kernel with singularities.
The last section is dedicated to define, using the truncated product rules constructed before, Nyström-type interpolants for a class of integral equations whose solution decay exponentially to a constant, at infinity, and to prove the stability and the convergence estimates for them. Numerical experiments are performed using Matlab, for a nontruncated product rule and for three particular truncated rules, obtaining an accuracy similar to that given by the complete rule.
The last section is dedicated to define, using the truncated product rules constructed before, Nyström-type interpolants for a class of integral equations whose solution decay exponentially to a constant, at infinity, and to prove the stability and the convergence estimates for them. Numerical experiments are performed using Matlab, for a nontruncated product rule and for three particular truncated rules, obtaining an accuracy similar to that given by the complete rule.
Reviewer: Iulian Coroian (Baia Mare)
MSC:
65D32 | Numerical quadrature and cubature formulas |
41A55 | Approximate quadratures |
45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
65R20 | Numerical methods for integral equations |