Hi,
problem:
the trapezoid method of solving differential equations is,
.
Since the method is implicit, we must solve for
on each step by some iterative method. If we use the fixed point iteration
, we know that the method will converge if
for
.
Give a condition on
such that the fixed point iteration converges at each step.
attempt:
First of all, I need to write down an expression for
. Fixed-point iteration needs an initial guess. I use
as my initial guess and write
as,
.
But now
,
which doesn't make much sense.
What am I doing wrong?
Thanks