Mercurial > repos > public > sbplib
diff +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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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk4/rungekutta_6.m Thu Sep 17 10:12:50 2015 +0200 @@ -0,0 +1,31 @@ +% Takes one time step of size k using the rungekutta method +% starting from v_0 and where the function F(v,t) gives the +% time derivatives. +function v = rungekutta_6(v, t , k, F) + s = 7 + k = zeros(length(v),s) + a = zeros(7,6); + c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1]; + b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12]; + a = [ + 0, 0, 0, 0, 0, 0; + 4/7, 0, 0, 0, 0, 0; + 115/112, -5/16, 0, 0, 0, 0; + 589/630, 5/18, -16/45, 0, 0, 0; + 229/1200 - 29/6000*sqrt(5), 119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5), 0, 0; + 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; + -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); + ] + + for i = 1:s + u = v + for j = 1: i-1 + u = u + h*a(i,j) * k(:,j) + end + k(:,i) = F(t+c(i)*k,u) + end + + for i = 1:s + v = v + k*b(i)*k(:,i) + end +end