Theory and Modern Applications
Table 5 The errors of the Runge-Kutta methods for ( 5.2 )
From: Asymptotical stability of Runge-Kutta for a class of impulsive differential equations
m | The implicit Euler | 2-Lobatto IIIA | 2-Lobatto IIIC | |||
|---|---|---|---|---|---|---|
AE | RE | AE | RE | AE | RE | |
100 | 0.0013 | 0.3930 | 2.5918e−006 | 8.0380e−004 | 5.2281e−006 | 0.0016 |
200 | 7.0145e−004 | 0.2175 | 6.4811e−007 | 2.0100e−004 | 1.3014e−006 | 4.0362e−004 |
400 | 3.6926e−004 | 0.1145 | 1.6204e−007 | 5.0254e−005 | 3.2470e−007 | 1.0070e−004 |
800 | 1.8947e−004 | 0.0588 | 4.0510e−008 | 1.2564e−005 | 8.1098e−008 | 2.5151e−005 |
1,600 | 9.5971e−005 | 0.0298 | 1.0128e−008 | 3.1409e−006 | 2.0265e−008 | 6.2848e−006 |
3,200 | 4.8298e−005 | 0.0150 | 2.5319e−009 | 7.8522e−007 | 5.0649e−009 | 1.5708e−006 |
Ratio | 1.9326 | 1.9227 | 3.9997 | 3.9997 | 4.0064 | 4.0064 |