Multivalue-multistage method for second-order ODEs
The aim of this paper is to generate the needed framework to develop order conditions for second-order Ordinary Differential Equations (ODEs) by class of multivalue-multistage Nystrom method. A general approach to study the order conditions of the methods for solving second-order initial value probl...
| Main Authors: | , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing
2016
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/57327/1/Multivalue-multistage%20method%20for%20second-order%20ODEs.pdf |
| _version_ | 1825931590586335232 |
|---|---|
| author | Ismail, Siti Ainathon Rabiei, Faranak |
| author_facet | Ismail, Siti Ainathon Rabiei, Faranak |
| author_sort | Ismail, Siti Ainathon |
| collection | UPM |
| description | The aim of this paper is to generate the needed framework to develop order conditions for second-order Ordinary Differential Equations (ODEs) by class of multivalue-multistage Nystrom method. A general approach to study the order conditions of the methods for solving second-order initial value problems is investigated. Our investigation will be carried out by adapting the theory of Nystrom-series and using the sets of second order rooted trees for solving second-order ODEs which leads to a general set of order conditions. In this paper the method of order three using constant step-size algorithm is derived. The stability region of method is also proposed. |
| first_indexed | 2024-03-06T09:29:03Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57327 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:29:03Z |
| publishDate | 2016 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | upm.eprints-573272017-09-26T04:04:33Z http://psasir.upm.edu.my/id/eprint/57327/ Multivalue-multistage method for second-order ODEs Ismail, Siti Ainathon Rabiei, Faranak The aim of this paper is to generate the needed framework to develop order conditions for second-order Ordinary Differential Equations (ODEs) by class of multivalue-multistage Nystrom method. A general approach to study the order conditions of the methods for solving second-order initial value problems is investigated. Our investigation will be carried out by adapting the theory of Nystrom-series and using the sets of second order rooted trees for solving second-order ODEs which leads to a general set of order conditions. In this paper the method of order three using constant step-size algorithm is derived. The stability region of method is also proposed. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57327/1/Multivalue-multistage%20method%20for%20second-order%20ODEs.pdf Ismail, Siti Ainathon and Rabiei, Faranak (2016) Multivalue-multistage method for second-order ODEs. In: 24th National Symposium on Mathematical Sciences (SKSM24), 27-29 Sept. 2016, Primula Beach Hotel, Kuala Terengganu, Terengganu. (pp. 1-5). 10.1063/1.4995927 |
| spellingShingle | Ismail, Siti Ainathon Rabiei, Faranak Multivalue-multistage method for second-order ODEs |
| title | Multivalue-multistage method for second-order ODEs |
| title_full | Multivalue-multistage method for second-order ODEs |
| title_fullStr | Multivalue-multistage method for second-order ODEs |
| title_full_unstemmed | Multivalue-multistage method for second-order ODEs |
| title_short | Multivalue-multistage method for second-order ODEs |
| title_sort | multivalue multistage method for second order odes |
| url | http://psasir.upm.edu.my/id/eprint/57327/1/Multivalue-multistage%20method%20for%20second-order%20ODEs.pdf |
| work_keys_str_mv | AT ismailsitiainathon multivaluemultistagemethodforsecondorderodes AT rabieifaranak multivaluemultistagemethodforsecondorderodes |