January 17th, 2016, 8:56 am
QuoteOriginally posted by: list1My original question was the meaning of the closed form solution. Others are not important@list is a stickler for definitions; it is not the first time that posters have been caught in his web. Reminds me of my Latin teacher.. You won't succeed:DAnyways, I see closed solution as u = F(parameters) where parameters do _not_ depend on u in any way. In theory we have an explicit solution for u. The function F can be anything.Examples1. du/dt + u = 0 for t > 0 with u(0) = 12. The 2d heat equation in a rectangle using separation of variables3. The GBM SDE with constant coefficientsNon-closed solutions1. Inverse normal CDF2. Nonlinear ODE and SDE3. General Navier-Stokes equation4. your example inverse function [$] y \, = \, F ( x ) \, = \, \int_0^{\lambda ( x )} f ( t ) \,dt [$].But, who knows, you might get lucky finding a closed solution.
Last edited by
Cuchulainn on January 16th, 2016, 11:00 pm, edited 1 time in total.