Research Article
A Class of Numerical Methods for the Solution of Fourth-Order Ordinary Differential Equations in Polar Coordinates
| | | 2nd-order method | 4th-order method | | | MAE | RMSE | MAE | RMSE |
| | | 0.7141 (−05) | 0.4859 (−05) | 0.2673 (−05) | 0.1818 (−05) | | 0.3339 (−05) | 0.2240 (−05) | 0.6974 (−06) | 0.4745 (−06) | | 0.2488 (−04) | 0.1683 (−04) | 0.1266 (−04) | 0.6538 (−05) | | 0.1126 (−04) | 0.8137 (−05) | 0.2548 (−05) | 0.1656 (−05) |
| | | 0.1806 (−05) | 0.1182 (−05) | 0.2467 (−06) | 0.1639 (−06) | | 0.8550 (−06) | 0.5595 (−06) | 0.4846 (−07) | 0.3212 (−07) | | 0.6486 (−05) | 0.4128 (−05) | 0.1167 (−05) | 0.5946 (−06) | | 0.2659 (−05) | 0.1957 (−05) | 0.1795 (−06) | 0.1119 (−06) |
| | | 0.4514 (−06) | 0.2917 (−06) | 0.2048 (−07) | 0.1346 (−07) | | 0.2152 (−06) | 0.1391 (−06) | 0.3315 (−08) | 0.2161 (−08) | | 0.1620 (−05) | 0.1020 (−05) | 0.1027 (−06) | 0.4911 (−07) | | 0.6757 (−06) | 0.4828 (−06) | 0.1222 (−07) | 0.7515 (−08) |
| | | 0.1125 (−06) | 0.7216 (−07) | 0.1510 (−08) | 0.9836 (−09) | | 0.5307 (−07) | 0.3442 (−07) | 0.2931 (−09) | 0.1883 (−09) | | 0.4038 (−06) | 0.2525 (−06) | 0.8190 (−08) | 0.3662 (−08) | | 0.1686 (−06) | 0.1192 (−06) | 0.9925 (−09) | 0.6537 (−09) |
| | | 0.3050 (−07) | 0.1946 (−07) | 0.1213 (−09) | 0.7945 (−10) | | 0.1461 (−07) | 0.9331 (−08) | 0.1358 (−10) | 0.8769 (−11) | | 0.1076 (−06) | 0.6812 (−07) | 0.6420 (−09) | 0.2913 (−09) | | 0.4591 (−07) | 0.3237 (−07) | 0.5009 (−10) | 0.3048 (−10) |
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