       NDSolve and Systems of DEs

• To: mathgroup at smc.vnet.net
• Subject: [mg74177] NDSolve and Systems of DEs
• From: "e-touch\ at libero\.it" <e-touch at libero.it>
• Date: Tue, 13 Mar 2007 04:03:54 -0500 (EST)

```Hello everybody!
In order to better understand the behaviour of NDSolve, I decided to try to=
solve a more simple system of equations...take a look here

eq1--d/dt p[x,t]==== k dd/dx2 p[x,t]
eq2--d/dt n[x,t]==== k dd/dx2 n[x,t]
eq3--d/dx El[x,t]====p[x,t]-n[x,t]
with:
p[x,0]====10*UnitStep[-x]; p[100,t]====0; p[-100,t]====10;
n[x,0]====10*UnitStep[x]; n[100,t]====10; n[-100,t]====0;
El[x,0]====0;

Eq1 and Eq2 are simple diffusion equations and El[x,t] it's just a function=
that I tried to couple with the other two...
All I get are error messages...
"NDSolve::pdord: Some of the functions have zero differential order so the =
\
equations will be solved as a system of differential-algebraic equations."
"NDSolve::bcart: Warning: An insufficient number of boundary conditions hav=
e \
been specified for the direction of independent variable x. Artificial \
boundary effects may be present in the solution."
"NDSolve::icfail: Unable to find initial conditions which satisfy the resid=
ual \
function within specified tolerances.  Try giving initial conditions for bo=
th \
values and derivatives of the functions."

The strange thing is that if I derive the funcion El[x,t] respect to time i=
nstead of x...so with
eq3--d/dt El[x,t]====p[x,t]-n[x,t];
El[x,0]====0;
...it works!!!
Could anyone explain this to me???
Thanks everybody
Matteo

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```

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