# NDSolve Systems of nonlinear coupled first order PDEs Covergence test failure

The system contains three nonlinear PDE with initial and boundary conditions.

NDSolve[{D[H[t, x], t] + D[u[t, x], x] H[t, x] + D[H[t, x], x] u[t, x] == 0,
- D[H[t, x], t] + D[v[t, x], x] (1 - H[t, x]) - D[H[t, x], x] v[t, x] == 0,
D[u[t, x], t] + u[t, x] D[u[t, x], x] == D[v[t, x], t] + v[t, x] D[v[t, x],x] ,
u[0, x] == 1, v[0, x] == 1, H[0, x] == 0.5, u[t, 1] == Cos[2 t],
v[t, 1] == Cos[t], H[t, 1] == 0.5 Cos[2 t]}, {u, v, H}, {t, 0,  10}, {x, 1, 10}]

But the error I got is shown as:

NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives.

NDSolve will try solving the system as differential-algebraic equations. NDSolve::ndcf: Repeated convergence test failure at t == 0.7337582610498328; unable to continue.

So, when I try to plot one solution component u[x,t]

Plot3D[Evaluate[u[t, x]], {t, 0, 0.5}, {x, 1, 10}]

I get empty box. Any idea?

• sol =NDSolve[...];,Plot3D[Evaluate[u[t, x]] /. sol, {t, 0, 0.5}, {x, 1, 10}] – Feyre Sep 9 '16 at 19:03
• Nope, it does not work either.. – Meva Sep 12 '16 at 8:11
• Nope, it does not work either.. I still got "NDSolve::ndcf: Repeated convergence test failure at t == 0.7337582610498328; unable to continue." error.. – Meva Sep 12 '16 at 8:24
• That wasn't meant to solve the error, just to allow you to plot to see what's going on. – Feyre Sep 12 '16 at 10:08