New versions of spline methods for integral equations of the third kind with singularities in the kernel. (English. Russian original) Zbl 1211.65174
Differ. Equ. 46, No. 9, 1330-1338 (2010); translation from Differ. Uravn. 46, No. 9, 1320-1328 (2010).
Summary: We analyze a linear integral equation of the third kind with fixed singularities in the kernel. For its generalized solution in the space of distributions, we suggest and justify new generalized versions of spline methods. We show that the constructed methods are order optimal.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
Keywords:
singular kernel; linear integral equation of the third kind; generalized solution; spline methodsReferences:
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