1
QI Using Crank-Nicolson F-D scheme, find U(x, 0. 1) for x = 0 3
2
and when U(x, t) satisfies
3
IJ(x, 0) = 18x(1 x), 0 < x < 1
(Use forward difference formula for derivative boundary condition)
(22. Derive the stability condition of the explicit F-D scheme when
applied to 0 < x < 1 with Ax = h , At = k and
, given that U(x, t) is known att = 0 and on x = 0 and
x = 1 for t > 0. (Use matrix method) (6M)
(23. Derive the local truncation error Tij when fully implicit
ðU 1 ô2 U
backward time scheme is applied to O < x < 1 with known initial and boundary values for U(x, t). (6M)
+ ( —vr)
2-
Scanned with CamScanner
