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...
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my-usm-ep.416942019-04-12T05:26:46Z Splines For Linear Two-Point Boundary Value Problems 2010-11 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 http://eprints.usm.my/41694/ http://eprints.usm.my/41694/1/Nur_Nadiah_Abd_Hamid_HJ.pdf application/pdf en public masters Universiti Sains Malaysia Pusat Pengajian Sains Matematik |
| institution |
Universiti Sains Malaysia |
| collection |
USM Institutional Repository |
| language |
English |
| topic |
QA101-145 Elementary Mathematics Arithmetic |
| spellingShingle |
QA101-145 Elementary Mathematics Arithmetic Hamid, Nur Nadiah Abd Splines For Linear Two-Point Boundary Value Problems |
| 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. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Hamid, Nur Nadiah Abd |
| author_facet |
Hamid, Nur Nadiah Abd |
| author_sort |
Hamid, Nur Nadiah Abd |
| title |
Splines For Linear Two-Point Boundary Value Problems |
| title_short |
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_sort |
splines for linear two-point boundary value problems |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2010 |
| url |
http://eprints.usm.my/41694/1/Nur_Nadiah_Abd_Hamid_HJ.pdf |
| _version_ |
1747820957327687680 |