Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86938/1/Numerical%20study%20of%20third-order%20ordinary%20differential%20equations.pdf http://psasir.upm.edu.my/id/eprint/86938/ https://www.sciencedirect.com/journal/alexandria-engineering-journal/vol/59/issue/4 |
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| Summary: | This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are validated by a number of various test problems and compared to existing methods in the literature. |
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