Collocation by singular splines

Splines determined by the kernel of the differential operator are known to be useful to solve the singular boundary value problems of the form . One of the most successful methods is the collocation method based on special Chebyshev splines. We investigate the construction of the associated B-splines based on knot-insertion algorithms for their evaluation, and their application in collocation at generalized Gaussian points. Specially, we show how to obtain these points as eigenvalues of a symmetric tridiagonal matrix of order k. This research was supported by Grant 037-1193086-2771, by the Ministry of science, education and sports of the Republic of Croatia.