Theory and Modern Applications
Table 1 The errors Runge–Kutta methods for (11)
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 | 0.02781 | 0.01871 | 7.58538e-04 | 5.10274e-04 | 5.35551e-07 | 3.60269e-07 |
20 | 0.01375 | 0.00925 | 1.94278e-04 | 1.30692e-04 | 3.36904e-08 | 2.26638e-08 |
40 | 0.00683 | 0.00460 | 4.91483e-05 | 3.30624e-05 | 2.11236e-09 | 1.42100e-09 |
80 | 0.00341 | 0.00229 | 1.23593e-05 | 8.31421e-06 | 1.32228e-10 | 8.89510e-11 |
160 | 0.00170 | 0.00114 | 3.09886e-06 | 2.08462e-06 | 8.26939e-12 | 5.56287e-12 |
Ratio | 2.01119 | 2.01119 | 3.95556 | 3.95556 | 15.95266 | 15.95266 |