Test solution of 1d Swift-Hohenberg equation
Test solution of 1d Swift-Hohenberg equation
In[]:=
Clear["Global`*"];
The usual form is u[x,t]==u[x,t]--2u[x,t]-u[x,t]Since there seems to be an issue with derivatives of order >2, I rewrote it as two coupled 2nd-order equations.It still gives a message saying it’s using the max. allowed 10000 grid points and then hangs for a long time.The actual solution is relatively smooth and, for example when solved by spectral methods, extremely fast to compute in 1d.
∂
t
3
u[x,t]
∂
x,x
∂
{x,4}
In[]:=
Clear["Global`*"];pde=u[x,t]==u[x,t]--2v[x,t]-v[x,t],v[x,t]==u[x,t];l=10;τ=10;bc={u[0,t]==u[l,t],v[0,t]==v[l,t]};init=u[x,0]==,v[x,0]==-;{usol,vsol}=NDSolveValue[{pde,bc,init},{u,v},{x,0,l},{t,0,τ}]
∂
t
3
u[x,t]
∂
x,x
∂
x,x
4x(l-x)
2
l
8
2
l
Out[]=
$Aborted