An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems
In this paper, we propose a new numerical scheme based on a variation of the standard formulation of the Runge–Kutta method using Taylor series expansion for solving initial value problems (IVPs) in ordinary differential equations. Analytically, the accuracy, consistency, and absolute stability of t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/17/3/123 |
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| author | Noori Y. Abdul-Hassan Zainab J. Kadum Ali Hasan Ali |
| author_facet | Noori Y. Abdul-Hassan Zainab J. Kadum Ali Hasan Ali |
| author_sort | Noori Y. Abdul-Hassan |
| collection | DOAJ |
| description | In this paper, we propose a new numerical scheme based on a variation of the standard formulation of the Runge–Kutta method using Taylor series expansion for solving initial value problems (IVPs) in ordinary differential equations. Analytically, the accuracy, consistency, and absolute stability of the new method are discussed. It is established that the new method is consistent and stable and has third-order convergence. Numerically, we present two models involving applications from physics and engineering to illustrate the efficiency and accuracy of our new method and compare it with further pertinent techniques carried out in the same order. |
| first_indexed | 2024-04-24T18:37:53Z |
| format | Article |
| id | doaj.art-95baa667354240f4aee57fa6e106dc60 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-04-24T18:37:53Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-95baa667354240f4aee57fa6e106dc602024-03-27T13:17:26ZengMDPI AGAlgorithms1999-48932024-03-0117312310.3390/a17030123An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value ProblemsNoori Y. Abdul-Hassan0Zainab J. Kadum1Ali Hasan Ali2Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, IraqBasrah Education Directorate, Ministry of Education, Basrah 61001, IraqDepartment of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, IraqIn this paper, we propose a new numerical scheme based on a variation of the standard formulation of the Runge–Kutta method using Taylor series expansion for solving initial value problems (IVPs) in ordinary differential equations. Analytically, the accuracy, consistency, and absolute stability of the new method are discussed. It is established that the new method is consistent and stable and has third-order convergence. Numerically, we present two models involving applications from physics and engineering to illustrate the efficiency and accuracy of our new method and compare it with further pertinent techniques carried out in the same order.https://www.mdpi.com/1999-4893/17/3/123numerical methodsinitial value problemautonomous equationlocal truncation errorconsistencystability |
| spellingShingle | Noori Y. Abdul-Hassan Zainab J. Kadum Ali Hasan Ali An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems Algorithms numerical methods initial value problem autonomous equation local truncation error consistency stability |
| title | An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems |
| title_full | An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems |
| title_fullStr | An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems |
| title_full_unstemmed | An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems |
| title_short | An Efficient Third-Order Scheme Based on Runge–Kutta and Taylor Series Expansion for Solving Initial Value Problems |
| title_sort | efficient third order scheme based on runge kutta and taylor series expansion for solving initial value problems |
| topic | numerical methods initial value problem autonomous equation local truncation error consistency stability |
| url | https://www.mdpi.com/1999-4893/17/3/123 |
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