suppressing evaluation/simplification in Integrate

• To: mathgroup at smc.vnet.net
• Subject: [mg45725] suppressing evaluation/simplification in Integrate
• From: Paul Holland <P.Holland at cpom.ucl.ac.uk>
• Date: Thu, 22 Jan 2004 03:37:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear MathGroup,

To model ice under ice shelves I am solving a set of 11 coupled PDEs
(varying in time and one spatial dimension) using NDSolve.  One of the
two spatial boundary conditions for each variable in this set of
equations involves an integral over time of a very involved function
which contains the Error or UnitStep functions applied to summations of
all 11 dependent variables and their spatial derivatives in various
involved combinations.

My problem is that when writing the boundary conditions to be put into
NDSolve, the Integrate function spends ages (longer than I have tried so
far - 4 days) trying to evaluate or simplify these complicated
integrals, when (at this stage) nothing is known about the variables and
therefore I know that Integrate won't be able to do anything.  Before
NDSolve is intitiated these integrals are purely symbolic; it is only
when NDSolve is solving the system of PDEs that this integral will be
possible to evaluate or simplify.

I know that this approach works in theory because I have been using it
for a long time with simpler integrals as the spatial boundary
condition.  Delaying the evaluation of the integral using ':=' is not
an option because Mathematica still needs to know what the boundary
conditions are before it enters the 'solve' part of NDSolve - if I use
:= then it is the NDSolve command which hangs rather than the
Integrate command preceeding it.

Therefore, I need to know if there is any way of just telling
Mathematica to 'read in' an Integral without trying to actually evaluate
it or simplify it.  It is only due to the complexity of the integrands
that the Integrate comand is taking so long trying to decide that they
are non-integrable - I know it won't actually be able to integrate them.
I have tried using the FullSimplify command before Integrate.

Any suggestions other than somehow suppressing Integrate's properties
are of course also welcome.

Many thanks,

Paul Holland

```

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