A Class of Numerical Methods for the Solution of Fourth-Order Ordinary Differential Equations in Polar Coordinates

Table 2

The MAE and RMSE.

		2nd-order method		4th-order method
ℎ		MAE	RMSE	MAE	RMSE
𝜆=1.0
1/8	𝑢	0.8435 (−04)	0.5652 (−04)	0.2744 (−05)	0.1880 (−05)
	𝑢^′	0.3552 (−03)	0.2322 (−03)	0.1058 (−04)	0.7178 (−05)
1/16	𝑢	0.2292 (−04)	0.1499 (−04)	0.1854 (−06)	0.1217 (−06)
	𝑢^′	0.7762 (−04)	0.5391 (−04)	0.6695 (−06)	0.4351 (−06)
1/32	𝑢	0.5844 (−05)	0.3771 (−05)	0.1151 (−07)	0.7446 (−08)
	𝑢^′	0.1885 (−04)	0.1322 (−04)	0.4115 (−07)	0.2618 (−07)
𝜆=100
1/8	𝑢	0.1961 (−02)	0.1401 (−02)	0.5662 (−04)	0.3877 (−04)
	𝑢^′	0.6514 (−02)	0.4687 (−02)	0.3824 (−03)	0.1910 (−03)
1/16	𝑢	0.4808 (−03)	0.3312 (−03)	0.3821 (−05)	0.2558 (−05)
	𝑢^′	0.1597 (−02)	0.1110 (−02)	0.1929 (−04)	0.9922 (−05)
1/32	𝑢	0.1197 (−03)	0.8103 (−04)	0.2435 (−06)	0.1609 (−06)
	𝑢^′	0.4023 (−03)	0.2714 (−03)	0.1135 (−05)	0.5843 (−06)