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comparison +time/+rk4/rungekutta_4RV.m @ 835:008496ca38f3 feature/burgers1d

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Compute the residual in between each runge-kutta stage. Note: It is not clear whether the correct residual is used when computing the stages. Must investigate further.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 13 Sep 2018 18:14:54 +0200
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children 619561e9ec0e
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834:f1f0bf087e1c 835:008496ca38f3
1 % Takes one time step of size k using the rungekutta method
2 % starting from v_0 and where the function F(v,t) gives the
3 % time derivatives.
4 function v = rungekutta_4RV(v, t , k, F, RV)
5 k1 = F(v, t, RV.getViscosity());
6
7 RV.update(v+0.5*k*k1, v, 0.5*k);
8 k2 = F(v+0.5*k*k1, t+0.5*k, RV.getViscosity());
9
10 RV.update(v+0.5*k*k2, v, 0.5*k);
11 k3 = F(v+0.5*k*k2, t+0.5*k, RV.getViscosity());
12
13 RV.update(v+k*k3, v, k);
14 k4 = F(v+k*k3,t+k, RV.getViscosity());
15
16 RV.update(v + (1/6)*(k1+2*(k2+k3)+k4)*k, v, k);
17 v = v + (1/6)*(k1+2*(k2+k3)+k4)*k;
18 end