Natural and Cardinal splines collocation method for the resolution of Fredholm integral equation of the second kind
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Date
2019
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Journal ISSN
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UNIVERSITE MOHAMED BOUDIAF - M’SILA- FACULTE MATHEMATIQUES ET DE L’INFORMATIQUE
Abstract
We have proposed two main methods, for approximating the solution of Fredholm linear integral equations of the second kind,based on cubic splines because of
their simplicity,stabilityand their high order of convergence. In spite of its positive
sounding name. the natural spline interpolation has little to recommend it from an
approximation theoretic point of view. Due to its global character and the fact that
the free-end conditions S
00 (a) = S
00 (b) = 0. produce an O (h
2
) error.The natural
spline interpolation method is complicated and requires many computations. However, the simulair results given for the method based on the cardinal spline are simple
and more closer to the exacte solution. Also , we veriÖed that the presented method
can be applied with large number of and remains stable.
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In the future, for a further research we hope to have a better comprehension, for splines and itís diverting types, that gives as a lot of doors to open in mathematics world.