Solving nonlinear system of third-order boundary value problems using block method
In this paper, we propose an algorithm of two-point block method to solve the nonlinear system of third-order boundary value problems directly. The proposed method is presented in a simple form of Adams type and two approximate solutions will be obtained simultaneously with the block method using va...
| Main Authors: | , , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57381/1/Solving%20nonlinear%20system%20of%20third-order%20boundary%20value%20problems%20using%20block%20method.pdf |
| _version_ | 1825931601260838912 |
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| author | Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed Ismail, Fudziah Othman, Khairil Iskandar |
| author_facet | Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed Ismail, Fudziah Othman, Khairil Iskandar |
| author_sort | Phang, Pei See |
| collection | UPM |
| description | In this paper, we propose an algorithm of two-point block method to solve the nonlinear system of third-order boundary value problems directly. The proposed method is presented in a simple form of Adams type and two approximate solutions will be obtained simultaneously with the block method using variable step size strategy. The method will be implemented with the multiple shooting technique via the three-step iterative method to generate the missing initial value. Most of the existence method will reduce the third-order boundary value problems to a system of first order equations where the systems of six equations need to be solved. The method we proposed in this paper will solve the third-order boundary value problems directly. Two numerical examples are given to illustrate the efficiency of the proposed method. |
| first_indexed | 2024-03-06T09:29:12Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57381 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:29:12Z |
| publishDate | 2014 |
| publisher | AIP Publishing LLC |
| record_format | dspace |
| spelling | upm.eprints-573812017-09-27T06:36:40Z http://psasir.upm.edu.my/id/eprint/57381/ Solving nonlinear system of third-order boundary value problems using block method Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed Ismail, Fudziah Othman, Khairil Iskandar In this paper, we propose an algorithm of two-point block method to solve the nonlinear system of third-order boundary value problems directly. The proposed method is presented in a simple form of Adams type and two approximate solutions will be obtained simultaneously with the block method using variable step size strategy. The method will be implemented with the multiple shooting technique via the three-step iterative method to generate the missing initial value. Most of the existence method will reduce the third-order boundary value problems to a system of first order equations where the systems of six equations need to be solved. The method we proposed in this paper will solve the third-order boundary value problems directly. Two numerical examples are given to illustrate the efficiency of the proposed method. AIP Publishing LLC 2014 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57381/1/Solving%20nonlinear%20system%20of%20third-order%20boundary%20value%20problems%20using%20block%20method.pdf Phang, Pei See and Abdul Majid, Zanariah and Suleiman, Mohamed and Ismail, Fudziah and Othman, Khairil Iskandar (2014) Solving nonlinear system of third-order boundary value problems using block method. In: International Conference on Mathematics, Engineering and Industrial Applications 2014 (ICoMEIA 2014), 28-30 May 2014, Penang, Malaysia. (pp. 1-7). 10.1063/1.4915691 |
| spellingShingle | Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed Ismail, Fudziah Othman, Khairil Iskandar Solving nonlinear system of third-order boundary value problems using block method |
| title | Solving nonlinear system of third-order boundary value problems using block method |
| title_full | Solving nonlinear system of third-order boundary value problems using block method |
| title_fullStr | Solving nonlinear system of third-order boundary value problems using block method |
| title_full_unstemmed | Solving nonlinear system of third-order boundary value problems using block method |
| title_short | Solving nonlinear system of third-order boundary value problems using block method |
| title_sort | solving nonlinear system of third order boundary value problems using block method |
| url | http://psasir.upm.edu.my/id/eprint/57381/1/Solving%20nonlinear%20system%20of%20third-order%20boundary%20value%20problems%20using%20block%20method.pdf |
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