|
RK4 |
RKF |
TR- |
Rosen- |
IMEX |
JVODE |
JVODE |
JLSODE |
|
|
|
BDF2 |
brock |
|
ADAMS |
BDF |
|
Protocol 1 (single pulse) |
Tol1 |
1.0 |
8.025e-3 |
3.587e-3 |
5.25e-4 |
5.22e-4 |
5.45e-4 |
8.83e-4 |
5.59e-4 |
Tol2 |
1.0 |
8.051e-3 |
1.8478 |
6.04e-4 |
5.76e-4 |
8.96e-4 |
1.163e-2 |
8.79e-4 |
ΔP1 Tol1/Tol2 |
- |
2.6e-5 |
1.8444 |
7.9e-5 |
5.4e-5 |
3.51e-4 |
1.075e-2 |
3.29e-4 |
Protocol 2 (repeated pulses) |
Tol1 |
1.0 |
8.034e-3 |
8.004e-3 |
5.74e-4 |
5.63e-4 |
6.76e-4 |
1.51e-3 |
6.6e-4 |
Tol2 |
1.0 |
8.067e-3 |
2.7826 |
8.04e-4 |
7.18e-4 |
1.554e-3 |
2.18e-2 |
1.35e-3 |
ΔP2 Tol1/Tol2 |
- |
3.3e-5 |
2.7746 |
2.3e-4 |
1.55e-4 |
8.68e-4 |
2.029e-2 |
6.92e-4 |
ΔTol1 P1/P2 |
- |
9.1e-6 |
4.417e-3 |
4.9e-5 |
4.1e-5 |
1.31e-4 |
6.27e-4 |
1.01e-4 |
Δ Tol2 P1/P2 |
- |
1.6e-6 |
0.9347 |
2.4e-4 |
1.42e-4 |
6.48e-4 |
1.016e-2 |
4.73e-4 |
Tol1 and Tol2 represent the ||p|| norm value for each algorithm with P1 and P2 protocols. ΔP1 Tol1/Tol2 represents the absolute difference between Tol1 and Tol2 for
P1, whereas ΔP2 Tol1/Tol2 represents the same absolute difference for P2. ΔTol1 P1/P2 represents the absolute difference between P1 and P2 for Tol1 parameters, whereas ΔTol2 P1/P2 represents the same absolute difference for Tol2. |