Last december I gave a talk about the Taylor series method for ordinary differential equations. See here and here for more informations. I put the slides for this talk online, as well as the source files which can be found here.
The Taylor series methods determines the solution of an ODE by its Taylor coefficients. The theory is extremely simple but the difficulty is to determine these coefficients numerically and in an unique way. To do so automatic differentiation is used where the formulas defining the ODE are given as expression trees and are then sequentially evaluated to obtain the n-the derivative or the n-th Taylor coefficient. Continue reading