Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti
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Convergence rates of some second and third order IMEX <strong>schemes</strong> <strong>for</strong> equilibrium initial<br />
data (dashed: v component, continuous: u component).<br />
Convergence rate<br />
Convergence rate<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
10 −6<br />
−0.5<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
10 −5<br />
−0.5<br />
10 −5<br />
10 −4<br />
10 −4<br />
10 −3<br />
SSP2−222<br />
10 −3<br />
Epsilon<br />
ARS−222<br />
Epsilon<br />
10 −2<br />
10 −2<br />
10 −1<br />
10 −1<br />
10 0<br />
10 0<br />
Convergence rate<br />
4<br />
3.5<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
10 −6<br />
−0.5<br />
Convergence rate<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
10 −6<br />
−0.5<br />
10 −5<br />
10 −5<br />
10 −4<br />
10 −4<br />
SSP3−332<br />
10 −3<br />
Epsilon<br />
SSP2−322<br />
10 −3<br />
Epsilon<br />
10 −2<br />
10 −2<br />
10 −1<br />
10 −1<br />
10 0<br />
10 0<br />
Convergence rate<br />
4<br />
3.5<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
10 −6<br />
−0.5<br />
Convergence rate<br />
3<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
10 −6<br />
−0.5<br />
10 −5<br />
10 −5<br />
10 −4<br />
10 −4<br />
SSP3−443<br />
10 −3<br />
Epsilon<br />
SSP2−332<br />
10 −3<br />
Epsilon<br />
10 −2<br />
10 −2<br />
10 −1<br />
10 −1<br />
10 0<br />
24<br />
10 0