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On the convergence of the spline collocation with discontinuous data
Author(s) -
Saranen J.,
Wendland W.
Publication year - 1987
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670090107
Subject(s) - mathematics , piecewise , sobolev space , collocation (remote sensing) , convergence (economics) , collocation method , spline (mechanical) , mathematical analysis , class (philosophy) , differential equation , ordinary differential equation , structural engineering , computer science , engineering , economics , economic growth , remote sensing , artificial intelligence , geology
In this article we study the convergence of the collocation method in the case where the smoothest splines are used as trial functions. The given data is allowed to be piecewise continuous. Our model problem is stated by means of an explicit Fourier representation in the space of periodic functions. Thus the results are applicable e.g. to differential operators and to classical integral operators of the convolutional type. Error estimates are given for a class of Sobolev norms. An application to the single layer potential is discussed.