# How to solve a system of PDAEs with eigenvalue

1. Nov 5, 2013

### ktsharp

I have the following system of partial differential algebraic equations:

[ tex ] \frac{1}{H_p}\frac{\partial H_p}{\partial t} = - \frac{\partial W_p}{\partial x} - \frac{f1(H_p,c_p,W_p)}{H_p}, [ \tex ]
$$\frac{1}{H_p}\frac{\partial}{\partial t}(H_p c_p} = - \frac{\partial}{\partial x}(W_p c_p) - \frac{f2(H_p,W_p,c_p)}{H_p}, [\tex] [tex] 0 = f2(H_p,c_p,W_p) + f3(H_p,c_p,W_p). [\tex] with the following conditions: Hp(x,0) = 5 Wp(x,0) = s1(x) cp(x,0) = s2(x) Hp(0,t) = s3(t) Wp(0,t) = W0 Wp(L,t) = 0 d(cp)/dx (L,t) = 0 How can I solve this numerically? 2. Nov 6, 2013 ### tiny-tim type "/tex" not "\tex" (or "") 3. Nov 6, 2013 ### ktsharp [UPDATED] I have the following system of partial differential algebraic equations: [tex] \frac{1}{H}\frac{\partial H}{\partial t} = - \frac{\partial W}{\partial x} - \frac{f_1(H,c,W)}{H},$$
$$\frac{1}{H}\frac{\partial}{\partial t}(H c) = - \frac{\partial}{\partial x}(W c) - \frac{f_2(H,W,c)}{H},$$
$$0 = f_2(H,c,W) + f_3(H,c,W).$$

with the following conditions:
H(x,0) = 5
W(x,0) = s1(x)
c(x,0) = s2(x)

H(0,t) = s3(t)
W(0,t) = W0
W(L,t) = 0
d(c)/dx (L,t) = 0

How can I solve this numerically?