ISSN:
0945-3245
Keywords:
AMS (MOS): 65D30
;
CR: G1.4
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In this paper we consider the approximate evaluation of $$\int\limits_a^b {K(x)f(x)dx} $$ , whereK(x) is a fixed Lebesgue integrable function, by product formulas of the form $$\sum\limits_{i = 0}^n {w_i f(x_i )} $$ based on cubic spline interpolation of the functionf. Generally, whenever it is possible, product quadratures incorporate the bad behaviour of the integrand in the kernelK. Here, however, we allowf to have a finite number of jump discontinuities in [a, b]. Convergence results are established and some numerical applications are given for a logarithmic singularity structure in the kernel.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01462239
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