       interpolating function as initial condition

• To: mathgroup at smc.vnet.net
• Subject: [mg102804] interpolating function as initial condition
• From: venkat reddy <vemkatma at gmail.com>
• Date: Thu, 27 Aug 2009 06:37:58 -0400 (EDT)

```* hi all,

I am relatively new to mathematica. I am trying to solve  4 couples pdes in
which one is second order pde. What I like to do is solve the equation
for some time span(like t=0 to t=tfinal) with some arbitray initial
conditions(e.g. cf[0,z]=tf[0,z]=something). I get solution for my 4
dependent variables(cf,tf,cc,tc) in terms of interpolated functions. I want
to use these interpolated functions as initial condition(like
cf[o,z]=InterpolatingFunction for  cf at tfinal) for further calculations=
. I
have trouble in using the interpolating function as initial condition.

Please can some body help me out.

Thank you.

here is the code for your reference

sol=NDSolve[

{

D[cf[t,z],t]+v D[cf[t,z],z]-a1 (cc[t,z]-cf[t,z])=C5 0,

D[tf[t,z],t]+v D[tf[t,z],z]-a2 (tc[t,z]-tf[t,z])-a3 (tw-tf[t,z])=C5 0,

D[cc[t,z],t]-a4 (cf[t,z]-cc[t,z])-a5 r[cc[t,z],tc[t,z]]=C5 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]=
=C5 0,

cf[t,0]=C5 c0,tf[t,0]=C5 t0,(D[tc[t,z],z]/.z=C2=AE0)=C5 0,(D[tc[t,z],=
z]/.z=C2=AElength)=C5 0,

cf[0,z]=C5 c0,tf[0,z]=C5 t0,cc[0,z]=C5 c0,tc[0,z]=C5 t0

},

{cf,tf,cc,tc},{t,0,tfinal}, {z,0,length}
]

{{cf=C2=AEInterpolatingFunction[{{0.,10000.},{0.,1.}},<>],

tf=C2=AEInterpolatingFunction[{{0.,10000.},{0.,1.}},<>],

cc=C2=AEInterpolatingFunction[{{0.,10000.},{0.,1.}},<>],

tc=C2=AEInterpolatingFunction[{{0.,10000.},{0.,1.}},<>]}}
*

```

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