Computational complexity for the two-point block method
In this paper, we discussed and compared the computational complexity for two-point block method and one-point method of Adams type. The computational complexity for both methods is determined based on the number of arithmetic operations performed and expressed in O(n). These two methods will be use...
| Main Authors: | , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2014
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/57350/ http://psasir.upm.edu.my/id/eprint/57350/1/Computational%20complexity%20for%20the%20two-point%20block%20method.pdf |
| _version_ | 1848853340937519104 |
|---|---|
| author | Phang, Pei See Abdul Majid, Zanariah |
| author_facet | Phang, Pei See Abdul Majid, Zanariah |
| author_sort | Phang, Pei See |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we discussed and compared the computational complexity for two-point block method and one-point method of Adams type. The computational complexity for both methods is determined based on the number of arithmetic operations performed and expressed in O(n). These two methods will be used to solve two-point second order boundary value problem directly and implemented using variable step size strategy adapted with the multiple shooting technique via three-step iterative method. Two numerical examples will be tested. The results show that the computational complexity of these methods is reliable to estimate the cost of these methods in term of the execution time. We conclude that the two-point block method has better computational performance compare to the one-point method as the total number of steps is larger. |
| first_indexed | 2025-11-15T10:52:25Z |
| format | Conference or Workshop Item |
| id | upm-57350 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:25Z |
| publishDate | 2014 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-573502017-09-26T04:10:00Z http://psasir.upm.edu.my/id/eprint/57350/ Computational complexity for the two-point block method Phang, Pei See Abdul Majid, Zanariah In this paper, we discussed and compared the computational complexity for two-point block method and one-point method of Adams type. The computational complexity for both methods is determined based on the number of arithmetic operations performed and expressed in O(n). These two methods will be used to solve two-point second order boundary value problem directly and implemented using variable step size strategy adapted with the multiple shooting technique via three-step iterative method. Two numerical examples will be tested. The results show that the computational complexity of these methods is reliable to estimate the cost of these methods in term of the execution time. We conclude that the two-point block method has better computational performance compare to the one-point method as the total number of steps is larger. AIP Publishing LLC 2014 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57350/1/Computational%20complexity%20for%20the%20two-point%20block%20method.pdf Phang, Pei See and Abdul Majid, Zanariah (2014) Computational complexity for the two-point block method. In: 3rd International Conference on Quantitative Sciences and Its Applications (ICOQSIA 2014), 12–14 Aug. 2014, Langkawi, Kedah. (pp. 187-194). 10.1063/1.4903582 |
| spellingShingle | Phang, Pei See Abdul Majid, Zanariah Computational complexity for the two-point block method |
| title | Computational complexity for the two-point block method |
| title_full | Computational complexity for the two-point block method |
| title_fullStr | Computational complexity for the two-point block method |
| title_full_unstemmed | Computational complexity for the two-point block method |
| title_short | Computational complexity for the two-point block method |
| title_sort | computational complexity for the two-point block method |
| url | http://psasir.upm.edu.my/id/eprint/57350/ http://psasir.upm.edu.my/id/eprint/57350/ http://psasir.upm.edu.my/id/eprint/57350/1/Computational%20complexity%20for%20the%20two-point%20block%20method.pdf |