Exponentially-fitted and trigonometrically-fitted two derivative Runge-Kutta-Nystrom methods for solving y''(x) = f(x, y, y' )
Two exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-Nyström (TDRKN) methods are being constructed. Exponentially fitted and trigonometrically fitted TDRKN methods have the favorable feature that they integrate exactly second-order systems whose solutions are lin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/72682/1/Exponentially%20fitted%20and%20trigonometrically%20fitted.pdf |
| Summary: | Two exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-Nyström (TDRKN) methods are being constructed. Exponentially fitted and trigonometrically fitted TDRKN methods have the favorable feature that they integrate exactly second-order systems whose solutions are linear combinations of functions {exp(wx),exp(-wx)} and {sin(wx),cos(wx)} respectively, when w∈R , the frequency of the problem. The results of numerical experiments showed that the new approaches are more efficient than existing methods in the literature. |
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