Re: NDSolve with integral equation
- To: mathgroup at smc.vnet.net
- Subject: [mg36165] Re: NDSolve with integral equation
- From: Bill Rowe <listuser at earthlink.net>
- Date: Mon, 26 Aug 2002 04:15:42 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On 8/23/02 at 12:25 AM, meshii at mech.fukui-u.ac.jp (Toshiyuki (Toshi)
Meshii) wrote:
>NDSolve seems to have difficulties with solving integral equation.
>n = 5; NDSolve[{D[\[Sigma]norm[z, t], t] ==
>3*z*Integrate[\[Sigma]norm[z, t]^n*z, {z, 0, 1}] - \[Sigma]norm[z,
>t]^n, \[Sigma]norm[z, 0] == 1.5*z, \[Sigma]norm[0, t] ==
>0}*\[Sigma]norm[z, t], {z, 0.01, 1}, {t, 0.01, 2}]
>Mathematica returns a message
>
>NDSolve::"deql": "The first argument must have both an equation and an
>\ initial condition."
A general solution to a differential equation includes a constant of integration. It isn't possible to arrive a numerical solution without providing sufficient information to determine this constant. Specifying the initial condition provides this information.
Look at the examples using the help browser to see what NDSolve needs.