Theory and Modern Applications
Table 2 The errors Runge–Kutta methods for (12)
From: Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations
m | Explicit Euler method | Ralston’s method | Classical fourth-order method | |||
|---|---|---|---|---|---|---|
AE | RE | AE | RE | AE | RE | |
10 | 0.00710 | 0.00635 | 3.89245e-05 | 3.48363e-05 | 3.99870e-09 | 3.57871e-09 |
20 | 0.00356 | 0.00319 | 9.81334e-06 | 8.78265e-06 | 2.61135e-10 | 2.33708e-10 |
40 | 0.00178 | 0.00160 | 2.46328e-06 | 2.20456e-06 | 1.66902e-11 | 1.49372e-11 |
80 | 8.92885e-04 | 7.99105e-04 | 6.17041e-07 | 5.52233e-07 | 1.05427e-12 | 9.43538e-13 |
160 | 4.46619e-04 | 3.99711e-04 | 1.54411e-07 | 1.38194e-07 | 6.55032e-14 | 5.86234e-14 |
Ratio | 1.99666 | 1.99666 | 3.98463 | 3.98463 | 15.72119 | 15.72119 |