Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince.
The Dormand-Prince method is a technique similar to the Runge-Kutta method for solving ordinary differential equations (ODEs). It uses six function evaluations to compute solutions with fourth and fifth-order accuracy. This study focuses on numerically solving first-order ODEs and systems of first-o...
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| Format: | Thesis |
| Language: | English |
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Kabale University
2024
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| Online Access: | http://hdl.handle.net/20.500.12493/2440 |
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| author | Byonaneebye, Darius |
| author_facet | Byonaneebye, Darius |
| author_sort | Byonaneebye, Darius |
| collection | KAB-DR |
| description | The Dormand-Prince method is a technique similar to the Runge-Kutta method for solving ordinary differential equations (ODEs). It uses six function evaluations to compute solutions with fourth and fifth-order accuracy. This study focuses on numerically solving first-order ODEs and systems of first-order ODEs using both the Runge-Kutta fourth-order method and the Dormand-Prince method. The solutions obtained from both methods are then compared in terms of their accuracy. MATLAB scripts for both methods were created to solve these differential equations. The study evaluates the accuracy of the Dormand-Prince method by comparing it with the Runge-Kutta fourth-order method. The results show that the Dormand-Prince method is more accurate than the Runge-Kutta fourth-order method when solving first-order ODEs. However, for systems of first-order ODEs, the Runge-Kutta method was found to be more accurate, while the Dormand-Prince method exhibited significant deviations from the analytical solution at various step sizes. Additionally, the accuracy of both methods improved as the step size decreased. |
| format | Thesis |
| id | oai:idr.kab.ac.ug:20.500.12493-2440 |
| institution | KAB-DR |
| language | English |
| publishDate | 2024 |
| publisher | Kabale University |
| record_format | dspace |
| spelling | oai:idr.kab.ac.ug:20.500.12493-24402024-12-19T00:00:47Z Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. Byonaneebye, Darius Comparative Analysis Fixed Variable Step Size Methods Solving Ordinary Differetial Equations Runge-Kutta Order 4 Dormand Prince The Dormand-Prince method is a technique similar to the Runge-Kutta method for solving ordinary differential equations (ODEs). It uses six function evaluations to compute solutions with fourth and fifth-order accuracy. This study focuses on numerically solving first-order ODEs and systems of first-order ODEs using both the Runge-Kutta fourth-order method and the Dormand-Prince method. The solutions obtained from both methods are then compared in terms of their accuracy. MATLAB scripts for both methods were created to solve these differential equations. The study evaluates the accuracy of the Dormand-Prince method by comparing it with the Runge-Kutta fourth-order method. The results show that the Dormand-Prince method is more accurate than the Runge-Kutta fourth-order method when solving first-order ODEs. However, for systems of first-order ODEs, the Runge-Kutta method was found to be more accurate, while the Dormand-Prince method exhibited significant deviations from the analytical solution at various step sizes. Additionally, the accuracy of both methods improved as the step size decreased. 2024-12-18T09:35:06Z 2024-12-18T09:35:06Z 2024 Thesis Byonaneebye, Darius (2024). Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. Kabale: Kabale University. http://hdl.handle.net/20.500.12493/2440 en application/pdf Kabale University |
| spellingShingle | Comparative Analysis Fixed Variable Step Size Methods Solving Ordinary Differetial Equations Runge-Kutta Order 4 Dormand Prince Byonaneebye, Darius Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. |
| title | Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. |
| title_full | Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. |
| title_fullStr | Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. |
| title_full_unstemmed | Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. |
| title_short | Comparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince. |
| title_sort | comparative analysis of fixed and variable step size methods for solving ordinary differetial equations a case study of runge kutta order 4 and dormand prince |
| topic | Comparative Analysis Fixed Variable Step Size Methods Solving Ordinary Differetial Equations Runge-Kutta Order 4 Dormand Prince |
| url | http://hdl.handle.net/20.500.12493/2440 |
| work_keys_str_mv | AT byonaneebyedarius comparativeanalysisoffixedandvariablestepsizemethodsforsolvingordinarydifferetialequationsacasestudyofrungekuttaorder4anddormandprince |