Suppose we want to solve the system of first order ODEs,
Here Y and A are n-vectors and
F is a nonlinear vector-valued
function on 
:
To insure existence and uniqueness of
a solution to (10) and hence establish
effective numerical procedures, we require that 
and
be continuous in the box
, 
where
and 
are positive numbers and 
is the vector
Euclidean norm. If 
for all 
in 
and if h is the smaller of
and 
, then the IVP (10) has a unique solution for
. Weaker conditions do exist, but these will suffice
for our purposes. For a more detailed discussion of existence and uniqueness
issues, consult any good text on differential equations, such as
[1,2,3].
