Question on Solving Differential Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg50403] Question on Solving Differential Equations
• From: "JJJ Shen" <jushen1 at hotmail.com>
• Date: Thu, 2 Sep 2004 04:34:28 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi, I'd like to ask a question on solving partial differential equations
using NDSolve:

-----------------------
Set of eqns:

I D[f[x,t], t] == - I D[f[x,t], x] + V DiracDelta[x] e[t];
I D[g[x,t], t] ==  I D[g[x,t], x] + V DiracDelta[x] e[t];
I D[e[t], t] == V f[0,t] + V g[0,t];

the 3rd equation can be written as

I D[e[t], t] == V NIntegrate[DiracDelta[x] f[x,t], {x,-0.001,0.001}] + V
NIntegrate[DiracDelta[x] g[x,t], {x,-0.001, 0.001}] ;

where the integration limit is chosen to fit the region of smoothed
DiracDelta function. V is a specified numerical constant.

Furthermore, since I couldn't get Mathematica to work with DiracDelta[x] in
NDSolve, I smoothed DiracDelta[x] by various functions conventionally used.
The initial conditions are also given: f[0,t], g[0,t], e[0].

----------------------

The problem is, Mathematica keeps complaining that the function e[t] does
not have x dependence:

NDSolve::derlen : The length of the derivative operator Derivative[1] in
e'[t] is not the same as the number of arguments.

I would appreciate any pointer to help get around of this complaint. Thanks
in advance.

JT

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```

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