Mercurial > repos > public > sbplib
comparison +time/+rk4/rungekutta_6.m @ 0:48b6fb693025
Initial commit.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Thu, 17 Sep 2015 10:12:50 +0200 |
| parents | |
| children | 1e057b0f2fed |
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| -1:000000000000 | 0:48b6fb693025 |
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| 1 % Takes one time step of size k using the rungekutta method | |
| 2 % starting from v_0 and where the function F(v,t) gives the | |
| 3 % time derivatives. | |
| 4 function v = rungekutta_6(v, t , k, F) | |
| 5 s = 7 | |
| 6 k = zeros(length(v),s) | |
| 7 a = zeros(7,6); | |
| 8 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1]; | |
| 9 b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12]; | |
| 10 a = [ | |
| 11 0, 0, 0, 0, 0, 0; | |
| 12 4/7, 0, 0, 0, 0, 0; | |
| 13 115/112, -5/16, 0, 0, 0, 0; | |
| 14 589/630, 5/18, -16/45, 0, 0, 0; | |
| 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; | |
| 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; | |
| 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); | |
| 18 ] | |
| 19 | |
| 20 for i = 1:s | |
| 21 u = v | |
| 22 for j = 1: i-1 | |
| 23 u = u + h*a(i,j) * k(:,j) | |
| 24 end | |
| 25 k(:,i) = F(t+c(i)*k,u) | |
| 26 end | |
| 27 | |
| 28 for i = 1:s | |
| 29 v = v + k*b(i)*k(:,i) | |
| 30 end | |
| 31 end |