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INTERNATIONAL JOURNAL OF SCIENTIFIC DEVELOPMENT AND RESEARCH International Peer Reviewed & Refereed Journals, Open Access Journal ISSN Approved Journal No: 2455-2631 | Impact factor: 8.15 | ESTD Year: 2016 open access , Peer-reviewed, and Refereed Journals, Impact factor 8.15 |
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| Paper Title: | New Higher Order Derivative Runge-Kutta Methods for Solving Ordinary Differential Equations |
| Authors Name: | Olaniyan A.S. , Akanbi M.A. , Oyewuwo F. R. |
| Unique Id: | IJSDR2304221 |
| Published In: | Volume 8 Issue 4, April-2023 |
| Abstract: | The derivation of numerical methods to deal with real life problems framed into differential equations has been on the increase of which good attention is directed to Runge-Kutta methods. Recently, researchers have explored the derivation of Runge-Kutta methods by introducing higher order derivative f^' (up to the second order) in the Runge-Kutta k_i terms (i>1) in order to increase the order of accuracy of the solution to the differential equation. However, this paper presents some new higher order derivative Runge-Kutta methods by using other types of ‘mean’ such as harmonic mean, geometric mean or harmonic mean as against the conventional Arithmetic mean viewed higher order derivative Runge-Kutta methods. The qualitative features such as the local truncation error, consistency, convergence and stability of the new methods are investigated and established. Numerical examples are used to compare the accuracies of these methods. The results show better performance of some of the derived methods when compared with existing methods. |
| Keywords: | Multiderivative, Harmonic Mean, Geometric Mean, Heronian Mean, Differential Equations |
| Cite Article: | "New Higher Order Derivative Runge-Kutta Methods for Solving Ordinary Differential Equations", International Journal of Science & Engineering Development Research (www.ijsdr.org), ISSN:2455-2631, Vol.8, Issue 4, page no.1368 - 1374, April-2023, Available :http://www.ijsdr.org/papers/IJSDR2304221.pdf |
| Downloads: | 000337072 |
| Publication Details: | Published Paper ID: IJSDR2304221 Registration ID:204868 Published In: Volume 8 Issue 4, April-2023 DOI (Digital Object Identifier): Page No: 1368 - 1374 Publisher: IJSDR | www.ijsdr.org ISSN Number: 2455-2631 |
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