Among the methods for solving equations of the form
with boundary conditions
and
at
is the Taylor series method, which uses the original equation to find
by repeatedly differentiating atfrom which we can write
Example: Solve
given
and
at
(1)
When
Differentiating (1) gives
(2) so when
Differentiating (2) gives
so when
Up to the term in
the solution is
