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diff +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
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line diff
--- a/+time/+rk4/rungekutta_6.m	Tue Sep 18 10:32:00 2018 +0200
+++ b/+time/+rk4/rungekutta_6.m	Wed Sep 19 16:32:05 2018 +0200
@@ -1,7 +1,7 @@
-% Takes one time step of size k using the rungekutta method
+% Takes one time step of size dt using the rungekutta method
 % starting from v_0 and where the function F(v,t) gives the
 % time derivatives.
-function v = rungekutta_6(v, t , k, F)
+function v = rungekutta_6(v, t , dt, F)
     s = 7
     k = zeros(length(v),s)
     a = zeros(7,6);
@@ -15,17 +15,17 @@
         229/1200 - 29/6000*sqrt(5),  119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5),        0,                 0;
         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;
         -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);
-    ]
+    ];
 
     for i = 1:s
-        u = v
-        for j = 1: i-1
-            u = u + h*a(i,j) * k(:,j)
+        u = v;
+        for j = 1:i-1
+            u = u + dt*a(i,j)*k(:,j);
         end
-        k(:,i) = F(t+c(i)*k,u)
+        k(:,i) = F(t+c(i)*dt,u);
     end
 
     for i = 1:s
-        v = v + k*b(i)*k(:,i)
+        v = v + dt*b(i)*k(:,i);
     end
 end