I'm having the following issue that can not find a solution , by using this boundary condition
u[0, t] == 1,
v[0, t] == u[1, t],
w[0, t] == v[1, t],
z[0, t] == w[1, t]
that Mathematica does not understand, someone please help me!
s = NDSolve[
{
D[u[x, t], t] == -D[u[x, t], x] - 1 v[x, t] w[x, t] z[x, t],
D[v[x, t], t] == -D[v[x, t], x] - 2 u[x, t] w[x, t] z[x, t],
D[w[x, t], t] == -D[w[x, t], x] - 3 u[x, t] v[x, t] z[x, t],
D[z[x, t], t] == -D[z[x, t], x] - 4 u[x, t] v[x, t] w[x, t],
u[x, 0] == 1,
v[x, 0] == 2,
w[x, 0] == 3,
z[x, 0] == 4,
u[0, t] == 1,
v[0, t] == u[1, t],
w[0, t] == v[1, t],
z[0, t] == w[1, t]
},
{u[x, t], v[x, t], w[x, t], z[x, t]},
{x, 0, 1}, {t, 0, 1}]
I'm getting this error message :
NDSolve::bcedge: Boundary condition v[0,t]==u[1,t] is not specified on a single edge of the boundary of the computational domain. >>
I have already presented a similar problem here, but the reasoning suggested is not a good solution for my case.
What strategies do you know to treat this problem ? I appreciate any help...
Attachments: