Selected problen1s 381- For the three-layer scherne
(^11) ,~t t = ()" I ' Yn xx + 1 + ( 1 ()" I _ ()" 2 ) Yn xx + ()" 2 ·yn xx - 1
a) investigate the approxinrn.tion error, b) find a stability condition, c)
impose the initial conditions yi^0 , y/, i = 0, 1, ... , N, not changing the order
of approxirnation for this proposal.
1 O. What differential equation is approximated by the difference equation
where I= r/h^2. Find the order of approximation for this.