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annotate +time/+rk4/rungekutta_6.m @ 87:0a29a60e0b21

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In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 29 Nov 2015 22:23:09 +0100
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