User talk:Celler

Does anyone know any papers that analyse the difference of the simulation results when modeling the same object but using different numerical methods( for example, different kinds of stiff and non-stiff solvers)?
 * Sri Kosuri 13:58, 29 August 2006 (EDT):Hi Celler... I don't know off the top of my head, but you should definitely check out Linda Petzold's work if you are interested in numerical method comparisons for ode integrators. if you are looking for integrators of stochatic differential equations, read dan gillespie's work.  I can give you more references if you are interested, but those are the places to start.
 * Sri Kosuri 13:58, 29 August 2006 (EDT):Just to point out, putting this question here will usually get no response. it's better to find a page that is appropriate to post a question such as this one.

Thanks very much for your reply. Which numerical method to use depends on the kind of system one need to integrate. I tried and found there's no big difference if using the appropriate methods. The slight difference lies in the speed and the accuracy you want to achieve. If the model is established well, you will get almost the same reasult with different numericial ODE Solvers. However, if some parameters are not set well, which might cause stiff problems, some Solver will fails to get the result. It is a quite complex issue. Here's a simple example:

->x1 x1->x2 x2->x3 x3->

dx1/dt = v1 -k1*x1 dx2/dt = k1*x1-k2*x2 dx3/dt = k2*x2 - k3*x3

Initial conditions

x1 = 1 x2 = 1e-8 x3 = 0

v1 = 1e-10 k1 = 1e20 k2 = 1 k3 = 1e20

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