Abstract
A class of L-splines is used to solve two-point boundary value problems. This class includes the set of Chebyshevian splines. The set of collocation points is a member of a general family related to the Gaussian points. We achieve the same order of convergence as for polynomial splines collocating at Gaussian points. A formula for the leading part of the error is found. An application is made to trigonometric splines. We show that these are useful in solving periodic boundary value problems.
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