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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universiti Kebangsaan Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/54939/1/A%20sixth-order%20RKFD%20method%20with%20four-stage%20for%20directly%20solving%20special%20fourth-order%20.pdf |
| 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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