Mercurial > repos > public > sbplib
diff +time/+rk/rungekutta.m @ 888:8732d6bd9890 feature/timesteppers
Add general Runge-Kutta class
- Add a general Runge-Kutta class which time integrates the solution based on coefficients obtained from a Butcher tableau
- Add butcher tableau which returns coefficents for the specified Runge-Kutta method
- Remove RungKutta4proper, since obsolete
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Thu, 15 Nov 2018 17:10:01 -0800 |
| parents | |
| children | 878652b22157 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk/rungekutta.m Thu Nov 15 17:10:01 2018 -0800 @@ -0,0 +1,20 @@ +% Takes one time step of size dt using the rungekutta method +% starting from @arg v and where the function F(v,t) gives the +% time derivatives. coeffs is a struct holding the RK coefficients +% for the specific method. +function v = rungekutta(v, t , dt, F, coeffs) + % Compute the intermediate stages k + k = zeros(length(v), coeffs.s); + for i = 1:coeffs.s + u = v; + for j = 1:i-1 + u = u + dt*coeffs.a(i,j)*k(:,j); + end + k(:,i) = F(u,t+coeffs.c(i)*dt); + end + % Compute the updated solution as a linear combination + % of the intermediate stages. + for i = 1:coeffs.s + v = v + dt*coeffs.b(i)*k(:,i); + end +end \ No newline at end of file