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annotate +time/+rk4/rungekutta_4RV.m @ 843:f63b99f0729d feature/burgers1d

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Minor rewrite of RK4RV
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 17 Sep 2018 11:08:23 +0200
parents 619561e9ec0e
children
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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
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f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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6 v1 = v + k/2*F(v,t, RV.getViscosity());
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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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7
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f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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8 RV.update(v1, v, k/2);
f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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9 v2 = v + k/2*F(v1,t+k/2, RV.getViscosity());
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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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10
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f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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11 RV.update(v2, v, k/2);
f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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12 v3 = v + k*F(v2,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
13
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f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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14 RV.update(v3,v,k);
f63b99f0729d Minor rewrite of RK4RV
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parents: 842
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15 v4 = v + k*F(v3,t+k, RV.getViscosity());
f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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f63b99f0729d Minor rewrite of RK4RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 842
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17 v_next = 1/6*(-3*v + 2*v1 + 4*v2 + 2*v3 + v4);
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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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18 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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19 v = v_next;
619561e9ec0e Reformulate the RK4 time stages in order to easier see how the residual should be updated.
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parents: 835
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20
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 % 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:
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22
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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23 % 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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24 % 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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25
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*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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27 % 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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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+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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30 % 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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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 + (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
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33 % 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:
diff changeset
34 end