Mercurial > repos > public > sbplib
comparison +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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| 887:50d5a3843099 | 888:8732d6bd9890 |
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| 1 % Takes one time step of size dt using the rungekutta method | |
| 2 % starting from @arg v and where the function F(v,t) gives the | |
| 3 % time derivatives. coeffs is a struct holding the RK coefficients | |
| 4 % for the specific method. | |
| 5 function v = rungekutta(v, t , dt, F, coeffs) | |
| 6 % Compute the intermediate stages k | |
| 7 k = zeros(length(v), coeffs.s); | |
| 8 for i = 1:coeffs.s | |
| 9 u = v; | |
| 10 for j = 1:i-1 | |
| 11 u = u + dt*coeffs.a(i,j)*k(:,j); | |
| 12 end | |
| 13 k(:,i) = F(u,t+coeffs.c(i)*dt); | |
| 14 end | |
| 15 % Compute the updated solution as a linear combination | |
| 16 % of the intermediate stages. | |
| 17 for i = 1:coeffs.s | |
| 18 v = v + dt*coeffs.b(i)*k(:,i); | |
| 19 end | |
| 20 end |