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

Table 1

The RMSE.

		2nd-order method		4th-order method
ℎ		MAE	RMSE	MAE	RMSE
1/8	𝑢	0.9512 (−03)	0.6737 (−03)	0.6018 (−03)	0.4089 (−03)
	𝑢^′	0.3162 (−02)	0.2137 (−02)	0.2961 (−02)	0.1402 (−02)
1/16	𝑢	0.2212 (−03)	0.1501 (−03)	0.3799 (−04)	0.2502 (−04)
	𝑢^′	0.7021 (−03)	0.4995 (−03)	0.3022 (−03)	0.9846 (−04)
1/32	𝑢	0.5410 (−04)	0.3576 (−04)	0.1989 (−05)	0.1304 (−05)
	𝑢^′	0.1729 (−03)	0.1206 (−03)	0.2302 (−05)	0.5629 (−05)
1/64	𝑢	0.1339 (−04)	0.8769 (−05)	0.9996 (−07)	0.6578 (−07)
	𝑢^′	0.4298 (−04)	0.2972 (−04)	0.1562 (−05)	0.2983 (−06)
1/128	𝑢	0.3363 (−05)	0.2174 (−05)	0.4198 (−08)	0.3345 (−08)
	𝑢^′	0.1072 (−04)	0.7383 (−05)	0.9892 (−07)	0.1538 (−07)