356 Difference Schemes with Constant Coefficients·-----· ·------· ·---·---·
(xi+1' tj) (xi-1,tj)a b c(xi, tj+1) (xi,tj+1)
·------· ·-------~·- (xi-1,tj) ·-------~•
d eFigure 17.
Having substituted (4) into (3), we obtainq = -1 ei'P +I + 1 = 1 + ( 1 - cos <p) r - i r sin <p
and find, by simple algebra, thatHence, I q I > 1 for any fixed I, bounded from below as T -+ oo, if sin <p /2 f::.
- It is worth noting here that the case where sin <p/2 = 0 corresponds to
the values y~ = 1 = canst. Then