MathGroup Archive 1998

[Date Index] [Thread Index] [Author Index]

Search the Archive

Parabolic equation in DSolve

Widely know that the solution
u[x,t]=1/(2K Sqrt[\pi t])Exp[-x^2/(4K^2 t)] is analitical result for
parabolic equation D[u[x,t],t]==K D[u[x,t],{x,2}]
u[x,0]== DiracDelta[x]

or in general formula
u[x,t]=1/(2K Sqrt[\pi t])Integrate[f[xx]Exp[-(x-xx)^2/(4K^2 t)],

but there is no way to find it in analytical.

I try
DSolve[D[f[x, t], t] ==K D[f[x, t], {x,2}], f[x,t], {x,t}]
and etc. with any initial and boundary conditions
{f[x,t]==DiracDelta[x], f[-Inf,t]==0,[+Inf,t]==0} don't give result or
"Partial differential equation may not have a general solution. Try
  Calculus`DSolveIntegrals` to find special solutions."

This way 
Derivative[0,1][f][x,t] == K Derivative[2,0][f][x,t],f[x,t], {x,t}] do
not give result too.

There is some result in numeriacal analys (from man) K=1;
solution=NDSolve[{D[f[x, t], t] ==K D[f[x, t], {x,2}],
    f[x, 0] == Exp[-x^2], f[-5, t] == f[5, t]},f, {x, -5, 5}, {t, 0,
5}]; Plot3D[Evaluate[f[x, t] /. First[solution]],{x,-5,5},{t,0,5},
but is any way fo find it result in analytic?


|       Vitali Ababi            |
| Physical Technical Department |
| Tomsk Polytechnic University  |
|     634004 Tomsk, Russia      |

  • Prev by Date: what does error msges means?
  • Next by Date: RE: New Notebook Select or Evaluation Command?
  • Previous by thread: what does error msges means?
  • Next by thread: Re: Mathematica and Win98?