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comparison +time/+rk4/rungekutta_4RV.m @ 843:f63b99f0729d feature/burgers1d

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Minor rewrite of RK4RV
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 17 Sep 2018 11:08:23 +0200
parents 619561e9ec0e
children
comparison
equal deleted inserted replaced
842:619561e9ec0e 843:f63b99f0729d
1 % Takes one time step of size k using the rungekutta method 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 2 % starting from v_0 and where the function F(v,t) gives the
3 % time derivatives. 3 % time derivatives.
4 function v = rungekutta_4RV(v, t , k, F, RV) 4 function v = rungekutta_4RV(v, t , k, F, RV)
5 5
6 6 v1 = v + k/2*F(v,t, RV.getViscosity());
7 v1 = v;
8 v2 = v1 + k/2*F(v1,t, RV.getViscosity());
9 7
10 RV.update(v2, v1, k/2); 8 RV.update(v1, v, k/2);
11 v3 = v1 + k/2*F(v2,t+k/2, RV.getViscosity()); 9 v2 = v + k/2*F(v1,t+k/2, RV.getViscosity());
12 10
13 RV.update(v3, v1, k/2); 11 RV.update(v2, v, k/2);
14 v4 = v1 + k*F(v3,t+k/2, RV.getViscosity()); 12 v3 = v + k*F(v2,t+k/2, RV.getViscosity());
15 13
16 RV.update(v4,v1,k); 14 RV.update(v3,v,k);
17 k4 = k*F(v4,t+k, RV.getViscosity()); 15 v4 = v + k*F(v3,t+k, RV.getViscosity());
18 16
19 v_next = 1/6*(-2*v1 + 2*v2 + 4*v3 + 2*v4 + k4); 17 v_next = 1/6*(-3*v + 2*v1 + 4*v2 + 2*v3 + v4);
20 RV.update(v_next,v,k); 18 RV.update(v_next,v,k);
21 v = v_next; 19 v = v_next;
22 20
23
24 % k1 = F(v, t, RV.getViscosity()); 21 % k1 = F(v, t, RV.getViscosity());
25 22
26 % RV.update(v+0.5*k*k1, v, 0.5*k); 23 % RV.update(v+0.5*k*k1, v, 0.5*k);
27 % k2 = F(v+0.5*k*k1, t+0.5*k, RV.getViscosity()); 24 % k2 = F(v+0.5*k*k1, t+0.5*k, RV.getViscosity());
28 25