From 5224b9052fe12a2cef798ab47b73f389d1bf7685 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian.jauslin@rutgers.edu>
Date: Wed, 17 May 2023 16:58:13 -0400
Subject: [PATCH] RKF45: use fourth order instead of fifth

---
 src/navier-stokes.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/navier-stokes.c b/src/navier-stokes.c
index 76b2bb2..0523bf5 100644
--- a/src/navier-stokes.c
+++ b/src/navier-stokes.c
@@ -712,7 +712,7 @@ int ns_step_rkf45(
       // difference between 5th order and 4th order
       err+=cabs((*delta)*(1./360*k1[klookup_sym(kx,ky,K2)]-128./4275*k3[klookup_sym(kx,ky,K2)]-2197./75240*k4[klookup_sym(kx,ky,K2)]+1./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]));
       // next step
-      tmp[klookup_sym(kx,ky,K2)]=(*delta)*(16./135*k1[klookup_sym(kx,ky,K2)]+6656./12825*k3[klookup_sym(kx,ky,K2)]+28561./56430*k4[klookup_sym(kx,ky,K2)]-9./50*k5[klookup_sym(kx,ky,K2)]+2./55*k6[klookup_sym(kx,ky,K2)]);
+      tmp[klookup_sym(kx,ky,K2)]=(*delta)*(25./216*k1[klookup_sym(kx,ky,K2)]+1408./2565*k3[klookup_sym(kx,ky,K2)]+2197./4104*k4[klookup_sym(kx,ky,K2)]-1./5*k5[klookup_sym(kx,ky,K2)]);
       relative+=cabs(tmp[klookup_sym(kx,ky,K2)]);
     }
   }