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annotate +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
parents
children 619561e9ec0e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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835
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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1 % Takes one time step of size k using the rungekutta method
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
2 % starting from v_0 and where the function F(v,t) gives the
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
3 % time derivatives.
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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4 function v = rungekutta_4RV(v, t , k, F, RV)
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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5 k1 = F(v, t, RV.getViscosity());
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
6
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
7 RV.update(v+0.5*k*k1, v, 0.5*k);
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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8 k2 = F(v+0.5*k*k1, t+0.5*k, RV.getViscosity());
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
9
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
10 RV.update(v+0.5*k*k2, v, 0.5*k);
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
11 k3 = F(v+0.5*k*k2, t+0.5*k, RV.getViscosity());
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
12
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
13 RV.update(v+k*k3, v, k);
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
14 k4 = F(v+k*k3,t+k, RV.getViscosity());
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
15
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
16 RV.update(v + (1/6)*(k1+2*(k2+k3)+k4)*k, v, k);
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
17 v = v + (1/6)*(k1+2*(k2+k3)+k4)*k;
008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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18 end