The solution of the initial value problem
for
,
is the logarithm , which is computed by time stepping
and extended to
by time stepping backwards in time t.
The logarithm is the inverse of the exponential
.
To do:
1. Play with the code changing into with C a given number.
2. Show that by construction
.
Hint: Show that if , then
(set
and note that
) and
. Conclude that
, that is
and so
, choosing
.
3. Show that log and exp are inverse functions (use that is the same as
).