Two Embedded Pairs of Runge-Kutta Type Methods for Direct Solution of Special Fourth-Order Ordinary Differential Equations

Table 1

The comparison results of the total number of successful steps and failure steps between RKFD6(), RKFD5(), RK6()V, and RK5()D methods for all problems.

Problems	Methods	Successful steps	Failure steps
1	RKFD6()	440	4
	RKFD5()	705	0
	RK6()V	461	9
	RK5()D	768	0
2	RKFD6()	151	0
	RKFD5()	200	0
	RK6()V	208	0
	RK5()D	253	0
3	RKFD6()	330	4
	RKFD5()	466	0
	RK6()V	348	8
	RK5()D	497	0
4	RKFD6()	264	5
	RKFD5()	340	6
	RK6()V	339	5
	RK5()D	484	5