Re: NDSolve and Systems of DEs

*To*: mathgroup at smc.vnet.net*Subject*: [mg74187] Re: NDSolve and Systems of DEs*From*: dh <dh at metrohm.ch>*Date*: Wed, 14 Mar 2007 03:41:20 -0500 (EST)*References*: <et5pgb$kao$1@smc.vnet.net>

Hi Matteo, here is you problem with corrected syntax: eqs={ D[p[x,t],t]==k D[ p[x,t],{x,2}], D[n[x,t],t]==k D[ p[x,t],{x,2}], D[ El[x,t],t]==p[x,t]-n[x,t], 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 }; k=1; NDSolve[eqs,{p[x,t],n[x,t], El[x,t]},{x,-100,100},{t,0,1}] However, nothe that it is not very clever to use the non-continuous UnitStep function in a numerical DE. Better use a continuos differentiable function like e.g. ArcTan. Daniel e-touch at libero.it wrote: > 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 > > > > ------------------------------------------------------ > Leggi GRATIS le tue mail con il telefonino i-mode=99 di Wind > http://i-mode.wind.it13mar07 > >