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comparison +time/+rk4/rungekutta_6.m @ 845:1e057b0f2fed feature/burgers1d

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Add RK6 with residual viscosity update and reduce computational effort of spatial scheme - Add RK6 with residual updates - Change the D2 operator for upwind schemes to one less computationally expensive.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 19 Sep 2018 16:32:05 +0200
parents 48b6fb693025
children
comparison
equal deleted inserted replaced
844:9e4e0576ca0f 845:1e057b0f2fed
1 % Takes one time step of size k using the rungekutta method 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 2 % starting from v_0 and where the function F(v,t) gives the
3 % time derivatives. 3 % time derivatives.
4 function v = rungekutta_6(v, t , k, F) 4 function v = rungekutta_6(v, t , dt, F)
5 s = 7 5 s = 7
6 k = zeros(length(v),s) 6 k = zeros(length(v),s)
7 a = zeros(7,6); 7 a = zeros(7,6);
8 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1]; 8 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
9 b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12]; 9 b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12];
13 115/112, -5/16, 0, 0, 0, 0; 13 115/112, -5/16, 0, 0, 0, 0;
14 589/630, 5/18, -16/45, 0, 0, 0; 14 589/630, 5/18, -16/45, 0, 0, 0;
15 229/1200 - 29/6000*sqrt(5), 119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5), 0, 0; 15 229/1200 - 29/6000*sqrt(5), 119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5), 0, 0;
16 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; 16 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;
17 -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); 17 -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);
18 ] 18 ];
19 19
20 for i = 1:s 20 for i = 1:s
21 u = v 21 u = v;
22 for j = 1: i-1 22 for j = 1:i-1
23 u = u + h*a(i,j) * k(:,j) 23 u = u + dt*a(i,j)*k(:,j);
24 end 24 end
25 k(:,i) = F(t+c(i)*k,u) 25 k(:,i) = F(t+c(i)*dt,u);
26 end 26 end
27 27
28 for i = 1:s 28 for i = 1:s
29 v = v + k*b(i)*k(:,i) 29 v = v + dt*b(i)*k(:,i);
30 end 30 end
31 end 31 end