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How to solve a system of PDAEs with eigenvalue

  1. Nov 5, 2013 #1
    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?
     
  2. jcsd
  3. Nov 6, 2013 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    type "/tex" not "\tex" (or "$$") :wink:
     
  4. Nov 6, 2013 #3
    [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}, [/tex]
    [tex] \frac{1}{H}\frac{\partial}{\partial t}(H c) = - \frac{\partial}{\partial x}(W c) - \frac{f_2(H,W,c)}{H}, [/tex]
    [tex] 0 = f_2(H,c,W) + f_3(H,c,W). [/tex]

    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?
     
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