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