A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs
In this article, the general form of Runge-Kutta method for directly solving a special fourth- order ordinary differential equations denoted as RKFD method is given. The order conditions up to order seven are derived, based on the order conditions, we construct a new explicit four-stage sixth-order...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2016
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| Online Access: | http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf http://journalarticle.ukm.my/10395/ http://www.ukm.my/jsm/english_journals/vol45num11_2016/contentsVol45num11_2016.html |
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| Summary: | In this article, the general form of Runge-Kutta method for directly solving a special fourth- order ordinary differential equations denoted as RKFD method is given. The order conditions up to order seven are derived, based on the order conditions, we construct a new explicit four-stage sixth-order RKFD method denoted as RKFD6 method. Zero-stability of the method is proven. Comparisons are made using the existing Runge–Kutta methods after the problems are reduced to a system of first order ordinary differential equations. Numerical results are presented to illustrate the efficiency and competency of the new method. |
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