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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