# Question:Numeric solve of a system with coupled pde/ode

## Question:Numeric solve of a system with coupled pde/ode

Maple 2018

I am studying the motion of a beam coupled to piezoelectric strips. This continuous system is modelled by two DE:

`YI*diff(w(x,t), x\$4)-N[0]*cos(2*omega*t)*diff(w(x,t), x\$2)+c*diff(w(x,t), t)+`&rho;A`*diff(w(x,t), t\$2)+C[em,m]*v(t) = 0;`

And:

`C[p]*diff(v(t), t)+1/R[l]*v(t) = C[em,e]*(D[1,2](w)(0,t)-D[1,2](w)(ell,t));`

where "w(x,t)" stands for the beam's vibration and "v(t)" means the electric voltage, which is constant throught the beam. I would like to numerically solve both DE simultaneosly, but maple will not let me do it. I would like to know why. I am getting the following error:

`Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same`

I suppose it is because "w(x,t)" depends on "x" and "t", while "v(t)" depends solely on time, but I am not sure. Could someone help me out? Here is my current code:

```restart:
with(PDEtools):
declare(w(x,t), v(t)):

YI*diff(w(x,t), x\$4)-N[0]*cos(2*omega*t)*diff(w(x,t), x\$2)+c*diff(w(x,t), t)+`&rho;A`*diff(w(x,t), t\$2)+C[em,m]*v(t) = 0;
pde1:= subs([YI = 1e4, N[0] = 5e3, c = 300, omega = 3.2233993, C[em,m] = 1], %):
ibc1:= w(0,t) = 0, D[1,1](w)(0,t) = 0, w(ell,t) = 0, D[1,1](w)(ell,t) = 0, D[2](w)(x,0) = 0, w(x,0) = sin(Pi*x/ell):

C[p]*diff(v(t), t)+1/R[l]*v(t) = C[em,e]*(D[1,2](w)(0,t)-D[1,2](w)(ell,t));
pde2:= subs([C[p] = 10, R[l] = 1000, C[em,e] = 1, ell = 5], %):
ibc2:= v(0) = 0:

pdsolve({pde1, pde2}, {ibc1, ibc2}, numeric);```

Thanks.

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