Re: Can I use Mathematica get the symbolic solution of PDEs without initial conditions?
- To: mathgroup at smc.vnet.net
- Subject: [mg41247] Re: Can I use Mathematica get the symbolic solution of PDEs without initial conditions?
- From: sean kim <shawn_s_kim at yahoo.com>
- Date: Sat, 10 May 2003 04:00:48 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
there are a number of pde's.
parabolic( heat eqns), elliptic(laplacian eqns), hyperbolic( wave
eqns).
which one are you considering solving?
and what does it mean when you say symbolic solutions without the
intial and boundary conditions? i can't think of a case where this is
possible....
then again i'm a newbie myself.
If you want solutions for all of them it will take a while. All of them
appears to be solvable numerically in mathematica. even if they are
complicated ( nonhomogenous, nonlinear etc etc) it might still be
possible to numerically approxinmate them.
get a book on numerical analysis using mathematica. there are a number
of them out there. i'm sure your school library has many as well. (
numerical solutions for partial differential euqations by ganzha and
vorozhtsov, or Partial differential equations and mathemtica by kythe,
puri and schaferkotter, or differential equations using mathemtica by
abell and braselton)
it also depends on how complicated your pde's are. Mine are systems
which makes analytical solution nonexistent, and they can only be
solved using numerical approximations.
starting with the simple parabolic form of the du/dt == d^2/dx^2.
this is refered to as the intial boundary value problem since it
contains both the intial conditions as well as the boundary conditions.
you need both the initial and boundary conditions as far as i know.
below solves it with intial and boundary conditions specified.
In[2]:=
u = y[x, t];
v6 = NDSolve[{D[u, t] == D[u, x, x],
y[x, 0] == If[Abs[x] < 2.99, E^(-x^2), 0], y[-10, t] == 0,
y[10, t] == 0}, y, {x, -10, 10}, {t, 0, 20}]
Plot3D[ Evaluate[y[x, t] /. v6 [[1]]], {x, -10, 10}, {t, 0, 20},
PlotPoints -> 30, PlotRange -> {0, 1}]
you can also use separation of variables and fourier sine series to
solve the above equation.
hope thats enough to start you off with
good luck
--- Chun Hua Lan <lan at zach.wustl.edu> wrote:
> Hi,
>
> I wonder that it is possible to get symbolic solution of a set of
> partial differential equations without initial condition and without
> boundary condition? If it is possible, would you please tell me the
>
> main command I had better use? Of course, if you have some programs
> related this, I will really appreciate that you can send to me. I am
>
> just a beginner.
>
>
> Thank you very much
>
> Lan
>
=====
when riding a dead horse, some dismount.
while others...
form a committee to examine the deadness of the horse, then form an oversight committee to examine the validity of the finding of the previous committee.
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