Hamid, Nur Nadiah Abd
(2010)
Splines For Linear TwoPoint Boundary Value Problems.
Masters thesis, Universiti Sains Malaysia.
Abstract
Linear twopoint boundary value problems of order two are solved using cubic trigonometric
Bspline, cubic Betaspline and extended cubic Bspline interpolation methods. Cubic
Betaspline has two shape parameters, b1 and b2 while extended cubic Bspline has one, l . In
this method, the parameters were varied and the corresponding approximations were compared
to the exact solution to obtain the best values of b1, b2 and l . The methods were tested on four
problems and the obtained approximated solutions were compared to that of cubic Bspline interpolation
method. Trigonometric Bspline produced better approximation for problems with
trigonometric form whereas Betaspline and extended cubic Bspline produced more accurate
approximation for some values of b1, b2 and l .
All in all, extended cubic Bspline interpolation produced the most accurate solution out
of the three splines. However, the method of finding l cannot be applied in the real world
because there is no exact solution provided. That method was implemented in order to test
whether values of l that produce better approximation do exist. Thus, an approach of finding
optimized l is developed and Newton’s method was applied to it. This approach was found to
approximate the solution much better than cubic Bspline interpolation method.
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