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.

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dc.contributor.authorByonaneebye, Darius
dc.date.accessioned2024-12-18T09:35:06Z
dc.date.available2024-12-18T09:35:06Z
dc.date.issued2024
dc.description.abstractThe 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.
dc.identifier.citationByonaneebye, 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.
dc.identifier.urihttp://hdl.handle.net/20.500.12493/2440
dc.language.isoen
dc.publisherKabale University
dc.subjectComparative Analysis
dc.subjectFixed
dc.subjectVariable Step Size Methods
dc.subjectSolving
dc.subjectOrdinary Differetial Equations
dc.subjectRunge-Kutta Order 4
dc.subjectDormand Prince
dc.titleComparative Analysis of Fixed and Variable Step Size Methods for Solving Ordinary Differetial Equations: A Case Study of Runge-Kutta Order 4 and Dormand Prince.
dc.typeThesis

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