- #1
ktsharp
- 8
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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 ]
[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?
[ 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 ]
[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?