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using interpolating function as initial condition to Ndsolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102766] using interpolating function as initial condition to Ndsolve
  • From: Santhosh <santhosh833 at gmail.com>
  • Date: Wed, 26 Aug 2009 07:45:23 -0400 (EDT)

hi all,

I am solving a set of four pdes (first order in time and second order
in space) using NDsolve. I am able to solve for arbitrary initial
conditions. What I am interested is fist solve with some random
initial conditions and get the steady state solution. I want to use
this solution as initial condition(e.g cf[0,z]=f(z)....) for the next
computations. I could not figure out how to use interpolating function
as initial condition.
can anybody have any idea?

Thank you.

here is my code
sol = NDSolve[
  			{
   				D[cf[t, z], t] + v D[cf[t, z], z] - a1 (cc[t, z] - cf[t, z]) ==
     0,
   				D[tf[t, z], t] + v D[tf[t, z], z] - a2 (tc[t, z] - tf[t, z]) -
     a3 (tw - tf[t, z]) == 0,
   D[cc[t, z], t] - a4 (cf[t, z] - cc[t, z]) -
     a5 r[cc[t, z], tc[t, z]] == 0,
   D[tc[t, z], t] - a6 (tf[t, z] - tc[t, z]) -
     a7 r[cc[t, z], tc[t, z]] - a8 D[tc[t, z], z, z] == 0,
   cf[t, 0] == c0,
   tf[t, 0] == t0, (D[tc[t, z], z] /. z -> 0) ==
    0, (D[tc[t, z], z] /. z -> length) == 0,
   cf[0, z] == c0, tf[0, z] == t0, cc[0, z] == c0, tc[0, z] == t0
                       },
     {cf, tf, cc, tc}, {t, 0, tfinal}, {z, 0, length}
  ]


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