Daniel, the solutions tend not to be dissipative. They are convective between regions, where the region boundaries are determined both exogenously (the different "tj's") and endogenously, by the value of psi = eta phi + eta x + dphi/dx passing the threshholds +/- epsilon. At the region boundaries, neither dphi/dx nor dphi/dt exists, but phi is continuous across the region boundaries. I suspect what I really need is a grid that knows to adjust to have edges at the boundary regions, and only requires continuity of phi but not dphi at those locations.
_____________________________________________ Douglas L. Borden Knight Equity Markets, L.P. 545 Washington Boulevard, Jersey City, NJ 07310 Tel: 201-239-2208 | Email: [email protected] Fax: 201-356-2279 | AIM: DBordenAtKnight Cell: 646-416-4875 | Skype: DBordenAtKnight LinkedIn: www.linkedin.com/in/douglasborden _____________________________________________ ________________________________ From: [email protected] [mailto:[email protected]] On Behalf Of Daniel Wheeler Sent: Thursday, October 15, 2009 11:21 AM To: Multiple recipients of list Subject: Re: Need help getting started Hi Doug, The only point I would add is to say that FiPy is really designed for convection-diffusion type problems. For pure convection problems that also have shocks, one needs specialized high order convection type terms to handle the sharp edges. I suspect that this will be the case with this equation. It does seem like it is possible to pose your system in FiPy with negative time, but I'm worried about the accuracy of the results. What sort of solutions does the equation give? Are they dissipative in nature? I'm trying to figure out whether our convection terms will be adequate, my initial feeling is that they won't be. On Tue, Oct 13, 2009 at 12:01 PM, Borden, Doug <[email protected]<mailto:[email protected]>> wrote: Hello, I've just started using FiPy for a problem in quantitative finance, and I need a bit of help getting started. I've cast a particular problem in trading as a stochastic control problem, and after deriving the relevant Hamilton-Jacobi-Bellman equation, I end up with a PDE to solve (see attached PDF). I have two questions: 1) Do I only have a source term and a transient term, or can I cast my problem with a convection term? 2) How do I specify my boundary conditions? Any help you can offer would be greatly appreciated. Best Regards, Doug Borden -------------------------------------------- Douglas L. Borden, Managing Director T: 201.239.2208 | F: 201.356.2279 | C: 646.416.4875 Email: [email protected]<mailto:[email protected]> | AIM: DBordenAtKnight LinkedIn: www.linkedin.com/in/douglasborden<http://www.linkedin.com/in/douglasborden> [cid:[email protected]] Knight Equity Markets, L.P. 545 Washington Boulevard | Jersey City, NJ 07310 -------------------------------------------- DISCLAIMER: This e-mail, and any attachments thereto, is intended only for use by the addressee(s)named herein and may contain legally privileged and/or confidential information. If you are not the intended recipient of this e-mail, you are hereby notified that any dissemination, distribution or copying of this e-mail and any attachments thereto, is strictly prohibited. If you have received this in error, please immediately notify me and permanently delete the original and any printout thereof. E-mail transmission cannot be guaranteed to be secure or error-free. The sender therefore does not accept liability for any errors or omissions in the contents of this message which arise as a result of e-mail transmission. NOTICE REGARDING PRIVACY AND CONFIDENTIALITY Knight Capital Group may, at its discretion, monitor and review the content of all e-mail communications. http://www.knight.com<http://www.knight.com/> -- Daniel Wheeler DISCLAIMER: This e-mail, and any attachments thereto, is intended only for use by the addressee(s)named herein and may contain legally privileged and/or confidential information. If you are not the intended recipient of this e-mail, you are hereby notified that any dissemination, distribution or copying of this e-mail and any attachments thereto, is strictly prohibited. If you have received this in error, please immediately notify me and permanently delete the original and any printout thereof. E-mail transmission cannot be guaranteed to be secure or error-free. The sender therefore does not accept liability for any errors or omissions in the contents of this message which arise as a result of e-mail transmission. NOTICE REGARDING PRIVACY AND CONFIDENTIALITY Knight Capital Group may, at its discretion, monitor and review the content of all e-mail communications. http://www.knight.com<http://www.knight.com/>
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