Taylor method is one of the best known one step method for solving ordinary differential equations numerically. The idea is to advance the solution using a truncated Taylor expansion of the variables about the current solution. Let
be an initial value problem and let h be the integration
step. To find 
, we expand 
around
and obtain
A numeric approximation of
is obtained by truncating (2)
at a pre-determined order.
The main problem connected with the Taylor method
is the need to compute higher derivatives
.
