Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations

Table 1

The test results for system (27).

		Maximum absolute error	Number of Newton iterations	Time
System (24)
	Step size
	BIRK	4.696875980934exp-02	999	0.0818
	SDIRK	2.951335592737exp-01	1002	0.0771
	SIRK	2.951335592737exp-01	1098	0.1158
	Gauss-IRK	4.696875980934exp-02	999	0.0801
	Step size
	BIRK	4.632141120340exp-03	1366	0.1015
	SDIRK	8.059127347433exp-02	1996	0.0941
	SIRK	8.059127347433exp-02	2100	0.1867
	Gauss-IRK	4.632141120340exp-03	1364	0.0949
	Step size
	BIRK	7.163047590741exp-06	5120	0.2795
	SDIRK	1.163100888497exp-03	5139	0.2143
	SIRK	1.163100888497exp-03	5276	0.4993
	Gauss-IRK	7.163047590741exp-06	5120	0.2769