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comparison +time/+rk/rungekutta.m @ 846:c6fcee3fcf1b feature/burgers1d

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Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 20 Sep 2018 17:51:19 +0200
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845:1e057b0f2fed 846:c6fcee3fcf1b
1 % Takes one time step of size dt using the rungekutta method
2 % starting from v_0 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