Next: Numerical Schemes
Up: Numerical Preliminaries
Previous: Numerical Preliminaries
  Contents
If we denote with
the function value at point of the
'the derivative of a function , then the Taylor series of a
continuous
function at point is given by:
|
(1.1) |
Some remarks about this expansion:
- can be any element of
, such that a function is
completely defined by its Taylor expansion at any single point of
its domain. (Full knowledge of the function at a single point
determines the full function at all points).
- The successive terms of the Taylor series are decreasing in
magnitude in an exponential way.
- We can truncate a Taylor series to approximate the original
function. This divides the Taylor series in two separate series:
the numerical scheme and the error series. The error after
truncation is mainly dependent on the first term of the error
series.
Next: Numerical Schemes
Up: Numerical Preliminaries
Previous: Numerical Preliminaries
  Contents
2002-11-15