| Author | Message | ||
     Eduards Rens (eduards) Member Username: eduards Post Number: 8 Registered: 12-2005 |
Can FlexPDE work with these two equations, how to define them in EQUATIONS section of script? 1. telegraph eq. Uxx = a^2* Utt + b* Ut + c* u 2. pseudo-parabolic eq. Ut = Uxxt + Uxx + f ? Regards, Eduards | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 848 Registered: 06-2003 |
In both cases, you need to define auxiliary variables to reduce each equation to second order. In the first equation, define a variable V=dt(U). Then substitute in equation 1, resulting in the system U: DT(U) = V V: a^2*DT(V) = DXX(U) - b*V + c*U The Natural BC for boundary flux must attach to the V equation, since that is now where the DXX() term is. See the discussion in "Samples | Time_Dependent | Stress | Vibrate.pde". The second equation presents more difficulty, because if you define V=UXX, one of the variables will not be marked by FlexPDE as requiring time integration, and the use of the time derivative of that variable may not work. One system to try would be U: DXX(U) = V V: DT(U) = DT(V) + V + F Notice that now the DXX(U) is in the U equation, and that equation must be assigned any NATURAL() boundary conditions. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 849 Registered: 06-2003 |
On second thought, maybe the way to handle problem 2 is the same as problem 1: Define V=DT(U) Then the system is U: DT(U) = V V: DXX(V) + DXX(U) + F = V The Natural BC for the V equation must now define the outward normal component of DX(V)+DX(U). NATURAL(V) = <uflux> + DX(V) |