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annotate +time/+rk4/rungekutta_6.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
parents 48b6fb693025
children 1e057b0f2fed
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1 % Takes one time step of size k using the rungekutta method
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2 % starting from v_0 and where the function F(v,t) gives the
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3 % time derivatives.
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4 function v = rungekutta_6(v, t , k, F)
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5 s = 7
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6 k = zeros(length(v),s)
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7 a = zeros(7,6);
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8 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
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9 b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12];
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10 a = [
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11 0, 0, 0, 0, 0, 0;
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12 4/7, 0, 0, 0, 0, 0;
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13 115/112, -5/16, 0, 0, 0, 0;
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14 589/630, 5/18, -16/45, 0, 0, 0;
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15 229/1200 - 29/6000*sqrt(5), 119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5), 0, 0;
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16 71/2400 - 587/12000*sqrt(5), 187/480 - 391/2400*sqrt(5), -38/75 + 26/375*sqrt(5), 27/80 - 3/400*sqrt(5), (1+sqrt(5))/4, 0;
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17 -49/480 + 43/160*sqrt(5), -425/96 + 51/32*sqrt(5), 52/15 - 4/5*sqrt(5), -27/16 + 3/16*sqrt(5), 5/4 - 3/4*sqrt(5), 5/2 - 1/2*sqrt(5);
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18 ]
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19
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20 for i = 1:s
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21 u = v
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22 for j = 1: i-1
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23 u = u + h*a(i,j) * k(:,j)
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24 end
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25 k(:,i) = F(t+c(i)*k,u)
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26 end
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27
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28 for i = 1:s
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29 v = v + k*b(i)*k(:,i)
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30 end
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31 end