# Get numerical solution of telegraph equation using NDSolve?

GROUPS:
 I am trying to get a numerical solution of the telegraph equation using NDSolve.Given a wire with resistance, inductivity and capacity per length of : r,l,c.We apply a voltage of ArcTan[20 t] 2/Pi to one end.The other end ist open. I first tried to model this condition by a NeumannValue, but Mathematica complains that the system ist overdetermined, what I do not understand. Amazingly it works without the NeumanValue, sort of.Here is the system: r = .1; l = 1; c = 1; tmax = 2.; eq = {D[u[x, t], {x, 2}] == r c D[u[x, t], t] + l c D[u[x, t], {t, 2}],u[0, t] == ArcTan[20 t] 2/Pi, u[x, 0] == 0}; res =u /. NDSolve[eq, {u}, {x, 0, 1}, {t, 0, tmax}][[1]] Plot3D[res[x, t], {x, 0, 1}, {t, 0, tmax}, AxesLabel -> Automatic] Up to tmax=2 I get reasonable results. But if tmax is larger, e.g. tmax=2.1, only garbage is returned. I tried all available options of NDSolve to get a stable integration, but failed.Can someone give a hint?Note that tmax=2 is the time when the wave is reflected a second time at x==0. I think the problem has to do with this reflection.
Answer
10 months ago