Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques
The two-point boundary value problems for the 4th order ordinarydifferential equations with a positive coefficient multiplying at least one of derivative terms are solved with two numerical methods. These numerical methods are the (Rung- Kutta of 4th Order) and (Rung –Kutta Butcher of 6th Order). Th...
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| Format: | Article |
| Language: | English |
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Unviversity of Technology- Iraq
2010-12-01
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| Series: | Engineering and Technology Journal |
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| Online Access: | https://etj.uotechnology.edu.iq/article_41766_23f8140f90df718e0f82fed93a754bfa.pdf |
| _version_ | 1797325296437821440 |
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| author | Anwar Mohamed Jawad |
| author_facet | Anwar Mohamed Jawad |
| author_sort | Anwar Mohamed Jawad |
| collection | DOAJ |
| description | The two-point boundary value problems for the 4th order ordinarydifferential equations with a positive coefficient multiplying at least one of derivative terms are solved with two numerical methods. These numerical methods are the (Rung- Kutta of 4th Order) and (Rung –Kutta Butcher of 6th Order). The 4th order ordinary differential Equations problem had been transformed to pair of second Order differential equations, which were solved together by the suggested methods. An initial value of the dependent variable had been predicted and corrected to some error. The two studied methods were tested on a physical model problem from the literature for comparing results.Solutions were presented in Tables and figures. good agreements were appeared in applying the studied methods |
| first_indexed | 2024-03-08T06:07:29Z |
| format | Article |
| id | doaj.art-5356420790984a2395c23a8c0a4a39d7 |
| institution | Directory Open Access Journal |
| issn | 1681-6900 2412-0758 |
| language | English |
| last_indexed | 2024-03-08T06:07:29Z |
| publishDate | 2010-12-01 |
| publisher | Unviversity of Technology- Iraq |
| record_format | Article |
| series | Engineering and Technology Journal |
| spelling | doaj.art-5356420790984a2395c23a8c0a4a39d72024-02-04T17:47:12ZengUnviversity of Technology- IraqEngineering and Technology Journal1681-69002412-07582010-12-0128247047705710.30684/etj.28.24.1841766Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher TechniquesAnwar Mohamed Jawad0Electrical and Electronic Engineering Department, University of Technology / BaghdadThe two-point boundary value problems for the 4th order ordinarydifferential equations with a positive coefficient multiplying at least one of derivative terms are solved with two numerical methods. These numerical methods are the (Rung- Kutta of 4th Order) and (Rung –Kutta Butcher of 6th Order). The 4th order ordinary differential Equations problem had been transformed to pair of second Order differential equations, which were solved together by the suggested methods. An initial value of the dependent variable had been predicted and corrected to some error. The two studied methods were tested on a physical model problem from the literature for comparing results.Solutions were presented in Tables and figures. good agreements were appeared in applying the studied methodshttps://etj.uotechnology.edu.iq/article_41766_23f8140f90df718e0f82fed93a754bfa.pdfboundary value problemsordinary differential equationbutcher |
| spellingShingle | Anwar Mohamed Jawad Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques Engineering and Technology Journal boundary value problems ordinary differential equation butcher |
| title | Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques |
| title_full | Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques |
| title_fullStr | Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques |
| title_full_unstemmed | Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques |
| title_short | Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques |
| title_sort | solving the boundary value problems of ordinary differential equation 4th order using rk4 and rk butcher techniques |
| topic | boundary value problems ordinary differential equation butcher |
| url | https://etj.uotechnology.edu.iq/article_41766_23f8140f90df718e0f82fed93a754bfa.pdf |
| work_keys_str_mv | AT anwarmohamedjawad solvingtheboundaryvalueproblemsofordinarydifferentialequation4thorderusingrk4andrkbutchertechniques |