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Math Help - Numerical solution of partial differential equation

  1. #1
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    Numerical solution of partial differential equation

    I need to solve the following system of equations for n=0,1,2 subject to the given initial and boundary conditions. Is it possible to solve the system numerically. If yes, please give me some idea which scheme I should use for better accuracy and how should I proceed. The coupled boundary conditions are challenging for me. Please help.


    \frac{\partial C_n}{\partial t}-\frac{\partial^2 C_n}{\partial r^2}-\frac{1}{r}\frac{\partial C_n}{\partial r}=\beta n\, f(y,t)C_{n-1}+n(n-1)C_{n-2}
    \frac{\partial \zeta_n}{\partial t}-\frac{\partial^2\zeta_n}{\partial r^2}-\frac{1}{r}\frac{\partial \zeta_n}{\partial r}=\beta n \,g(y,t)\zeta_{n-1}+n(n-1)\zeta_{n-2}

    C_n(0,y)=1 \quad\mbox{for}\quad n=0
    =0 \quad\mbox{for}\quad n>0

    \zeta_n(0,y)=1 \quad\mbox{for}\quad n=0
    \quad\quad\quad=0 \quad\mbox{for}\quad n>0

    \frac{\partial C_n}{\partial r}+\gamma C_n=0 \quad\mbox{at}\quad  r=a
    \frac{\partial C_n}{\partial r}=\kappa \frac{\partial \zeta_n}{\partial r} \quad\mbox{at}\quad r=b
    C_n=\lambda\zeta_n \quad\mbox{at}\quad r=b
    \frac{\partial \zeta_n}{\partial r}=0 \quad\mbox{at}\quad r=0
    Last edited by Suvadip; October 27th 2013 at 10:36 AM.
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  2. #2
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    Re: Numerical solution of partial differential equation

    read r in place of y
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