Variable order step size algorithm for solving second order ODEs
Previous multi step method using a divided difference formulation for solving higher order ordinary differential equations (ODEs) requires calculating the integration co-efficients at every step. In the current research, a multi step method in backwards difference form is established. The backward differe...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Book Section |
| Language: | English |
| Published: |
UPM Press
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/79017/ http://psasir.upm.edu.my/id/eprint/79017/1/2019-chapterinbookvariablenocover.pdf |
| _version_ | 1848858575343976448 |
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| author | Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hassan Wong, Tze Ji Koo, Lee Feng |
| author2 | Asbullah, Muhammad Asyraf |
| author_facet | Asbullah, Muhammad Asyraf Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hassan Wong, Tze Ji Koo, Lee Feng |
| author_sort | Rasedee, Ahmad Fadly Nurullah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Previous multi step method using a divided difference formulation for solving higher order ordinary differential equations (ODEs) requires calculating the integration co-efficients at every step. In the current research, a multi step method in backwards difference form is established. The backward difference formulation offers a solution to the tedious calculation of integration coefficients. Rather than calculating inte-gration coefficients at every step change, a backward difference formulation requires calculating integration coefficients only once in the beginning and if required once more at the end. The proposed method will also be equipped with a variable order step size algorithm to reduce computational cost (calculation time). Both linear and nonlinear second order ODEs will used to validate the accuracy and efficiency of the proposed method. |
| first_indexed | 2025-11-15T12:15:37Z |
| format | Book Section |
| id | upm-79017 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:15:37Z |
| publishDate | 2019 |
| publisher | UPM Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-790172021-08-03T23:24:20Z http://psasir.upm.edu.my/id/eprint/79017/ Variable order step size algorithm for solving second order ODEs Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hassan Wong, Tze Ji Koo, Lee Feng Previous multi step method using a divided difference formulation for solving higher order ordinary differential equations (ODEs) requires calculating the integration co-efficients at every step. In the current research, a multi step method in backwards difference form is established. The backward difference formulation offers a solution to the tedious calculation of integration coefficients. Rather than calculating inte-gration coefficients at every step change, a backward difference formulation requires calculating integration coefficients only once in the beginning and if required once more at the end. The proposed method will also be equipped with a variable order step size algorithm to reduce computational cost (calculation time). Both linear and nonlinear second order ODEs will used to validate the accuracy and efficiency of the proposed method. UPM Press Asbullah, Muhammad Asyraf Hafidzuddin, Mohd Ezad Hafidz 2019 Book Section PeerReviewed text en http://psasir.upm.edu.my/id/eprint/79017/1/2019-chapterinbookvariablenocover.pdf Rasedee, Ahmad Fadly Nurullah and Abdul Sathar, Mohamad Hassan and Wong, Tze Ji and Koo, Lee Feng (2019) Variable order step size algorithm for solving second order ODEs. In: Embracing Mathematical Diversity: Selected papers from Seminar on Mathematical Sciences 2019 (SOMS2019). UPM Press, Malaysia, 158 - 167. ISBN 9789672395089 file:///C:/Users/User/Downloads/2019-chapterinbookvariablenocover.pdf |
| spellingShingle | Rasedee, Ahmad Fadly Nurullah Abdul Sathar, Mohamad Hassan Wong, Tze Ji Koo, Lee Feng Variable order step size algorithm for solving second order ODEs |
| title | Variable order step size algorithm for solving second order ODEs |
| title_full | Variable order step size algorithm for solving second order ODEs |
| title_fullStr | Variable order step size algorithm for solving second order ODEs |
| title_full_unstemmed | Variable order step size algorithm for solving second order ODEs |
| title_short | Variable order step size algorithm for solving second order ODEs |
| title_sort | variable order step size algorithm for solving second order odes |
| url | http://psasir.upm.edu.my/id/eprint/79017/ http://psasir.upm.edu.my/id/eprint/79017/ http://psasir.upm.edu.my/id/eprint/79017/1/2019-chapterinbookvariablenocover.pdf |