New Phase Fitted and Amplification Fitted Numerov-Type Methods for Periodic IVPs with Two Frequencies

Table 1

Comparison of the end-point global errors and the consumed CPU time in seconds (in the brackets) produced by the five methods for Problem 1.

ℎ	EFRKN4F	VPHA	TFNTONE	PFAFI	PFAFII
1	NaN (0.09)	674.5 (0.08)	63.2 (0.06)	0.27 (0.06)	7.9e − 3 (0.06)
1/2	0.17 (1.19)	12.7 (0.13)	1.99 (0.11)	0.04 (0.13)	1.3e − 3 (0.11)
1/4	4.6e − 3 (0.34)	2.3e − 2 (0.28)	2.7e − 3 (0.23)	1.5e − 4 (0.23)	1.1e − 5 (0.23)
1/8	1.5e − 4 (0.71)	2.4e − 4 (0.53)	2.8e − 5 (0.47)	2.3e − 6 (0.48)	1.9e − 7 (0.48)
1/16	0.7e − 6 (1.39)	3.4e − 6 (1.13)	1.43e − 7 (0.95)	1.3×10^−7 (0.95)	4.9e − 9 (0.95)