de solvers and richardson extrapolation

Posted by Sashan Govender on Jan 03, 2007; 2:10am
URL: http://quantlib.414.s1.nabble.com/de-solvers-and-richardson-extrapolation-tp11396.html

Hi

I downloaded quantlib and had a look at the euler solver
(expliciteuler.hpp) but all I can find is the interface to the class.
I can't find the implementation, the code that does f(x + h) = h*f'(x)
+ f(x). I've implemented some numercial ode solvers in some work I did at
university in physically based animation and am curious about applications in
financial mathematics.

I had a look at the todo list and it mentioned richardson
extrapolation. I have rough plan for implementing this so that it can
handle any solver (ie. Euler, RK4 etc...). The basic idea is that the
solver classes define methods that return the value of the
approximation A (see
http://en.wikipedia.org/wiki/Richardson_extrapolation for definition)
and the class that performs Richardson's extrapolation defines a
method to apply the recurrance relation (defined in the above link)
for a single time step. Since the approximation A differs depending on
the type of the solver used this approach will not constrict the class
that implements the Richardson extrapolation to a specific ODE solver.

I can detail this approach with some C++ code hopefully sometime soon.

--
sashan
http://sashang.orcon.net.nz