Research Article
New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs
Table 4
Numerical results for Problem
1 to Problem
8 with
.
| | Problem | | DIRKN4(3)6 | DIRKN4(3)8 | PFRKN | RKND |
| | 1 | 0.025 | 3.641739(−2) | 5.515151(−4) | 7.685603(−3) | 3.246585(−1) | | 0.0125 | 1.121169(−3) | 1.412513(−5) | 2.381676(−4) | 2.064614(−2) | | 0.00625 | 3.522474(−5) | 3.162919(−6) | 8.044719(−6) | 1.293771(−3) |
| | 2 | 0.25 | 4.968941(−3) | 8.176026(−5) | 1.059320(−3) | 4.581100(−2) | | 0.125 | 1.553957(−4) | 2.266041(−6) | 3.290638(−5) | 2.860912(−3) | | 0.0625 | 4.858102(−6) | 3.894456(−8) | 1.025317(−6) | 1.789827(−4) |
| | 3 | 0.025 | 5.050886(−2) | 7.713254(−4) | 1.065804(−2) | 4.502978(−1) | | 0.0125 | 1.554479(−3) | 1.993991(−5) | 3.302186(−4) | 2.863241(−2) | | 0.00625 | 4.884725(−5) | 4.407458(−6) | 1.114967(−5) | 1.794225(−3) |
| | 4 | 0.025 | 5.050886(−2) | 7.713235(−4) | 1.065799(−2) | 4.502978(−1) | | 0.0125 | 1.554479(−3) | 1.993979(−5) | 3.302153(−4) | 2.863241(−2) | | 0.00625 | 4.884726(−5) | 4.407458(−6) | 1.114963(−5) | 1.794225(−3) |
| | 5 | 0.25 | 3.142511(−5) | 2.225689(−6) | 5.906399(−6) | 7.329390(−5) | | 0.125 | 9.872922(−7) | 1.311623(−7) | 2.060768(−7) | 4.155967(−6) | | 0.0625 | 3.122323(−8) | 7.739299(−9) | 8.477345(−9) | 4.155967(−6) |
| | 6 | 0.025 | 8.130019(−1) | 5.143138(−3) | 6.323161(−2) | 1.581409(−1) | | 0.0125 | 7.270152(−3) | 1.088848(−4) | 1.513299(−3) | 6.194539(−2) | | 0.00625 | 2.200129(−4) | 3.162925(−6) | 4.672316(−5) | 4.048100(−3) |
| | 7 | 0.2 | 3.103741(−3) | 4.927970(−5) | 6.483674(−4) | 1.326941(−2) | | 0.1 | 9.720586(−5) | 1.472241(−6) | 1.980997(−5) | 8.293575(−4) | | 0.05 | 3.068984(−6) | 7.146919(−8) | 6.187652(−7) | 5.183626(−5) |
| | 8 | 0.004 | 2.227290(−6) | 2.224132(−6) | 1.495525(−5) | 1.548512(−5) | | 0.002 | 1.231234(−5) | 1.231204(−5) | 1.310806(−5) | 1.314136(−5) | | 0.001 | 1.735729(−5) | 1.735723(−5) | 1.740702(−5) | 1.740910(−5) |
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