New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs

Table 3

The DIRKN4(3)8New method.

𝑐1	𝜆
1/2−√3/6	(1/6−√3/12−𝜆)	𝜆
(1/2+√3/6)	0	(1/6+√3/12−𝜆)	𝜆
1/2−√3/6	0	0	(1/6−√3/12−𝜆)	𝜆
	0	𝑏2	1/4−√3/12	𝑏4
	0	0	1/2	1/2
	𝑏̂^′1	𝑏̂^′2	0.108	0.14
	0	0.22	0.5	0.28

Where 𝑐₁=−0.1704903206, 𝑏₂=0.2332957499, 𝑏₄=0.1610418175, 𝑏̂^′₁=0.00353468159, 𝑏̂^′₂=0.24846531841 and 𝜆=2𝜆²=0.01453347471.