       Re: NDSolve initial value problem

• To: mathgroup at smc.vnet.net
• Subject: [mg99239] Re: NDSolve initial value problem
• From: dh <dh at metrohm.com>
• Date: Thu, 30 Apr 2009 06:25:45 -0400 (EDT)
• References: <gt90l4\$l1t\$1@smc.vnet.net>

```
Hi Murat,

the solution to your DEQ must be continuous. Therefore,

T[0,y]==Piecewise[{0,-1< y<1}]==0 (where I delete the superfluous part) and:

T[x, 1] == 1 for x==0

are inconsistent.

Daniel

Murat HavzalÄ± wrote:

> Dear Mathematica users;

>

>

>

> I am trying to solve liquid heat/mass transfer equation with mixed boundary

> conditions.

>

> My code looks like this:

>

>

>

> pe=0.5;

>

> u[y]=1-y^2;

>

>

>

> sol=NDSolve[

>

> {

>

> pe*u[y]*D[T[x,y],x]==D[T[x,y],y,y],

>

>

>

> T[0,y]==Piecewise[{{-y,y<=-1},{0,-1< y<1},{1,1<=y}}],

>

>

>

> T[x,1]==1,

>

> (D[T[x,y],y]/.y->-1)==-1

>

>

>

> },

>

> T,{x,0,1},{y,-1,1},SolveDelayed->True];

>

>

>

> This returns inconsistent initial boundary conditions error.

>

> I also tried to make the piecewise initial condition, a numerical function

> namely:

>

>

>

> initial[y_?NumericQ]:=Piecewise[{{-y,y<=-1},{0,-1< y<1},{1,1<=y}}]

>

>

>

>

>

> However this did not work, too. I understand that there is a similar

>

> and I tried my best to convert it to my problem but couldn't. I couldn't

> find the code but I also tried to give the

>

> initial piecewise function as a interpolating function, it returned the same

> response.

>

> Any help would be appreciated.

>

>

>

> Thanks.

>

>

>

> Murat Havzal

>

>

```

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