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annotate +time/+rk4/rungekutta_4RV.m @ 842:619561e9ec0e feature/burgers1d

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Reformulate the RK4 time stages in order to easier see how the residual should be updated.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 14 Sep 2018 16:40:19 +0200
parents 008496ca38f3
children f63b99f0729d
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:
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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:
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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)
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619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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5
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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6
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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7 v1 = v;
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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8 v2 = v1 + k/2*F(v1,t, RV.getViscosity());
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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9
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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10 RV.update(v2, v1, k/2);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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11 v3 = v1 + k/2*F(v2,t+k/2, RV.getViscosity());
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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12
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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13 RV.update(v3, v1, k/2);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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14 v4 = v1 + k*F(v3,t+k/2, RV.getViscosity());
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008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
15
842
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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16 RV.update(v4,v1,k);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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17 k4 = k*F(v4,t+k, RV.getViscosity());
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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18
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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19 v_next = 1/6*(-2*v1 + 2*v2 + 4*v3 + 2*v4 + k4);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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20 RV.update(v_next,v,k);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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21 v = v_next;
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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22
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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23
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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24 % k1 = F(v, t, RV.getViscosity());
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008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
25
842
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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26 % RV.update(v+0.5*k*k1, v, 0.5*k);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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27 % k2 = F(v+0.5*k*k1, t+0.5*k, RV.getViscosity());
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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28
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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29 % RV.update(v+0.5*k*k2, v, 0.5*k);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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30 % k3 = F(v+0.5*k*k2, t+0.5*k, RV.getViscosity());
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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31
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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32 % RV.update(v+k*k3, v, k);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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33 % k4 = F(v+k*k3,t+k, RV.getViscosity());
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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34
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
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35 % RV.update(v + (1/6)*(k1+2*(k2+k3)+k4)*k, v, k);
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 835
diff changeset
36 % v = v + (1/6)*(k1+2*(k2+k3)+k4)*k;
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008496ca38f3 Compute the residual in between each runge-kutta stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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37 end