Theory and Modern Applications
Table 4 The errors of the Runge-Kutta methods for ( 5.1 )
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 | |
10 | 0.2731 | 2.1864 | 0.0023 | 0.0188 | 0.0049 | 0.0393 |
20 | 0.0956 | 0.7651 | 5.8209 | 0.0047 | 0.0012 | 0.0096 |
40 | 0.0406 | 0.3251 | 1.4524e−004 | 0.0012 | 2.9546e−004 | 0.0024 |
80 | 0.0188 | 0.1504 | 3.6293e−005 | 2.9057e−004 | 7.3237e−005 | 5.8636e−004 |
160 | 0.0090 | 0.0724 | 9.0721e−006 | 7.2634e−005 | 1.8227e−005 | 1.4594e−004 |
320 | 0.0044 | 0.0355 | 2.2680e−006 | 1.8158e−005 | 4.5464e−006 | 3.6400e−005 |
Ratio | 2.2977 | 2.2977 | 4.0083 | 4.0083 | 4.0435 | 4.0435 |