Numerical solution of second order ordinary differential equations
Numerical analysis is a modern technology employed by scientists and engineers to tackle complex problems that are challenging to solve through direct methods. In this article, we introduce the Milne-Simpson predictor-corrector technique (MS) and the fourth-order Adam-Bashforth-Moulton predictor-cor...
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| Format: | Article |
| Language: | English |
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REA Press
2024-12-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_206026_6d4f6686e45234907366ea6048244528.pdf |
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| author | Ayokunle Tadema |
| author_facet | Ayokunle Tadema |
| author_sort | Ayokunle Tadema |
| collection | DOAJ |
| description | Numerical analysis is a modern technology employed by scientists and engineers to tackle complex problems that are challenging to solve through direct methods. In this article, we introduce the Milne-Simpson predictor-corrector technique (MS) and the fourth-order Adam-Bashforth-Moulton predictor-corrector method (ADM) for solving second-order initial value problems (IVPs) of ordinary differential equations.Both methods are highly efficient and particularly suitable for addressing IVPs. We compare the Euler and fourth-order Runge-Kutta methods within the ADM framework to the Milne-Simpson predictor-corrector approach. To validate the accuracy of the numerical solutions, we compare the approximate solutions with the exact solutions and find that they align well. We also observe that initializing the fourth-order ADM method with the fourth-order Runge-Kutta method and using the MS method for approximation yields superior accuracy compared to starting the ADM with the Euler method. Additionally, we evaluate the performance, effectiveness, and computational efficiency of both approaches. Finally, we demonstrate the convergence of these methods and examine the error terms for various step sizes. The numerical experiments are conducted using Matlab 2024. |
| format | Article |
| id | doaj-art-afab083ea73c4534adea33cdd64a2392 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-afab083ea73c4534adea33cdd64a23922025-01-30T11:23:34ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202024-12-013427729010.22105/cand.2024.479470.1152206026Numerical solution of second order ordinary differential equationsAyokunle Tadema0Department of Mathematics, University of lbadan, lbadan Nigeria.Numerical analysis is a modern technology employed by scientists and engineers to tackle complex problems that are challenging to solve through direct methods. In this article, we introduce the Milne-Simpson predictor-corrector technique (MS) and the fourth-order Adam-Bashforth-Moulton predictor-corrector method (ADM) for solving second-order initial value problems (IVPs) of ordinary differential equations.Both methods are highly efficient and particularly suitable for addressing IVPs. We compare the Euler and fourth-order Runge-Kutta methods within the ADM framework to the Milne-Simpson predictor-corrector approach. To validate the accuracy of the numerical solutions, we compare the approximate solutions with the exact solutions and find that they align well. We also observe that initializing the fourth-order ADM method with the fourth-order Runge-Kutta method and using the MS method for approximation yields superior accuracy compared to starting the ADM with the Euler method. Additionally, we evaluate the performance, effectiveness, and computational efficiency of both approaches. Finally, we demonstrate the convergence of these methods and examine the error terms for various step sizes. The numerical experiments are conducted using Matlab 2024.https://www.journal-cand.com/article_206026_6d4f6686e45234907366ea6048244528.pdfadam-bashforth-moulton predictor-corrector methodinitial value problems (ivp)euler methodrunge kutta methodmilne simpson predictor-corrector method |
| spellingShingle | Ayokunle Tadema Numerical solution of second order ordinary differential equations Computational Algorithms and Numerical Dimensions adam-bashforth-moulton predictor-corrector method initial value problems (ivp) euler method runge kutta method milne simpson predictor-corrector method |
| title | Numerical solution of second order ordinary differential equations |
| title_full | Numerical solution of second order ordinary differential equations |
| title_fullStr | Numerical solution of second order ordinary differential equations |
| title_full_unstemmed | Numerical solution of second order ordinary differential equations |
| title_short | Numerical solution of second order ordinary differential equations |
| title_sort | numerical solution of second order ordinary differential equations |
| topic | adam-bashforth-moulton predictor-corrector method initial value problems (ivp) euler method runge kutta method milne simpson predictor-corrector method |
| url | https://www.journal-cand.com/article_206026_6d4f6686e45234907366ea6048244528.pdf |
| work_keys_str_mv | AT ayokunletadema numericalsolutionofsecondorderordinarydifferentialequations |