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...
| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2010
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| Online Access: | http://eprints.usm.my/41694/1/Nur_Nadiah_Abd_Hamid_HJ.pdf |
| _version_ | 1797010681088704512 |
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| author | Hamid, Nur Nadiah Abd |
| author_facet | Hamid, Nur Nadiah Abd |
| author_sort | Hamid, Nur Nadiah Abd |
| collection | USM |
| description | 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. |
| first_indexed | 2024-03-06T15:23:20Z |
| format | Thesis |
| id | usm.eprints-41694 |
| institution | Universiti Sains Malaysia |
| language | English |
| last_indexed | 2024-03-06T15:23:20Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | usm.eprints-416942019-04-12T05:26:46Z http://eprints.usm.my/41694/ Splines For Linear Two-Point Boundary Value Problems Hamid, Nur Nadiah Abd QA101-145 Elementary Mathematics, Arithmetic 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. 2010-11 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/41694/1/Nur_Nadiah_Abd_Hamid_HJ.pdf Hamid, Nur Nadiah Abd (2010) Splines For Linear Two-Point Boundary Value Problems. Masters thesis, Universiti Sains Malaysia. |
| spellingShingle | QA101-145 Elementary Mathematics, Arithmetic Hamid, Nur Nadiah Abd Splines For Linear Two-Point Boundary Value Problems |
| title | Splines For Linear Two-Point Boundary Value Problems |
| title_full | Splines For Linear Two-Point Boundary Value Problems |
| title_fullStr | Splines For Linear Two-Point Boundary Value Problems |
| title_full_unstemmed | Splines For Linear Two-Point Boundary Value Problems |
| title_short | Splines For Linear Two-Point Boundary Value Problems |
| title_sort | splines for linear two point boundary value problems |
| topic | QA101-145 Elementary Mathematics, Arithmetic |
| url | http://eprints.usm.my/41694/1/Nur_Nadiah_Abd_Hamid_HJ.pdf |
| work_keys_str_mv | AT hamidnurnadiahabd splinesforlineartwopointboundaryvalueproblems |