Splines For Linear Two-Point Boundary Value Problems
Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline, cubic Beta-spline and extended cubic B-spline interpolation methods. Cubic Beta-spline has two shape parameters, b1 and b2 while extended cubic B-spline has one, l . In this method, the parameters...
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis |
| Language: | English |
| Published: |
2010
|
| Subjects: | |
| Online Access: | http://eprints.usm.my/41694/1/Nur_Nadiah_Abd_Hamid_HJ.pdf http://eprints.usm.my/41694/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Linear two-point boundary value problems of order two are solved using cubic trigonometric
B-spline, cubic Beta-spline and extended cubic B-spline interpolation methods. Cubic
Beta-spline has two shape parameters, b1 and b2 while extended cubic B-spline 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 B-spline interpolation
method. Trigonometric B-spline produced better approximation for problems with
trigonometric form whereas Beta-spline and extended cubic B-spline produced more accurate
approximation for some values of b1, b2 and l .
All in all, extended cubic B-spline 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 B-spline interpolation method. |
|---|