Numerical solution of higher order ordinary differential equations by direct block code
Problem statement: This study is concerned with the development of a code based on 2-point block method for solving higher order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) directly. Approach: The block method was developed based on numerical integration and using interpo...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Science Publications
2012
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/25314/1/jmssp.2012.77.81.pdf |
| _version_ | 1796970734280507392 |
|---|---|
| author | Waeleh, Nazreen Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed |
| author_facet | Waeleh, Nazreen Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed |
| author_sort | Waeleh, Nazreen |
| collection | UPM |
| description | Problem statement: This study is concerned with the development of a code based on 2-point block method for solving higher order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) directly. Approach: The block method was developed based on numerical integration and using interpolation approach which is similarly as Adams Moulton type. Furthermore, the proposed method is derived in order to solve higher order ODEs in a single code using variable step size and implemented in a predictor corrector mode. This block method will act as simultaneous numerical integrator by computing the numerical solution at two steps simultaneously. Results: The numerical results for the direct block method were superior compared to the existing block method. Conclusion: It is clearly proved that the code is able to produce good results for solving higher order ODEs. |
| first_indexed | 2024-03-06T08:02:28Z |
| format | Article |
| id | upm.eprints-25314 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:02:28Z |
| publishDate | 2012 |
| publisher | Science Publications |
| record_format | dspace |
| spelling | upm.eprints-253142017-09-28T03:19:33Z http://psasir.upm.edu.my/id/eprint/25314/ Numerical solution of higher order ordinary differential equations by direct block code Waeleh, Nazreen Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed Problem statement: This study is concerned with the development of a code based on 2-point block method for solving higher order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) directly. Approach: The block method was developed based on numerical integration and using interpolation approach which is similarly as Adams Moulton type. Furthermore, the proposed method is derived in order to solve higher order ODEs in a single code using variable step size and implemented in a predictor corrector mode. This block method will act as simultaneous numerical integrator by computing the numerical solution at two steps simultaneously. Results: The numerical results for the direct block method were superior compared to the existing block method. Conclusion: It is clearly proved that the code is able to produce good results for solving higher order ODEs. Science Publications 2012 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25314/1/jmssp.2012.77.81.pdf Waeleh, Nazreen and Abdul Majid, Zanariah and Ismail, Fudziah and Suleiman, Mohamed (2012) Numerical solution of higher order ordinary differential equations by direct block code. Journal of Mathematics and Statistics, 8 (1). pp. 77-81. ISSN 1549-3644; ESSN: 1558-6359 http://thescipub.com/abstract/10.3844/jmssp.2012.77.81 10.3844/jmssp.2012.77.81 |
| spellingShingle | Waeleh, Nazreen Abdul Majid, Zanariah Ismail, Fudziah Suleiman, Mohamed Numerical solution of higher order ordinary differential equations by direct block code |
| title | Numerical solution of higher order ordinary differential equations by direct block code |
| title_full | Numerical solution of higher order ordinary differential equations by direct block code |
| title_fullStr | Numerical solution of higher order ordinary differential equations by direct block code |
| title_full_unstemmed | Numerical solution of higher order ordinary differential equations by direct block code |
| title_short | Numerical solution of higher order ordinary differential equations by direct block code |
| title_sort | numerical solution of higher order ordinary differential equations by direct block code |
| url | http://psasir.upm.edu.my/id/eprint/25314/1/jmssp.2012.77.81.pdf |
| work_keys_str_mv | AT waelehnazreen numericalsolutionofhigherorderordinarydifferentialequationsbydirectblockcode AT abdulmajidzanariah numericalsolutionofhigherorderordinarydifferentialequationsbydirectblockcode AT ismailfudziah numericalsolutionofhigherorderordinarydifferentialequationsbydirectblockcode AT suleimanmohamed numericalsolutionofhigherorderordinarydifferentialequationsbydirectblockcode |