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