Appendix
Numerical Miscellany
A.l Finite-Difference Operator Notation
Complex finite-difference formulae are written in compact form using the following operator notation, which is similar to that used in Shuman and Hovermale
(1968):
{,nx f (x) =
fex + nl:i.xj2) - fex - nl:i.xj2)
"--------'-----''------'-n Sx
(A.I)
and
nx
(f(x))
=
fex + nl:i.xj2) + fex - nl:i.xj2)
2
.
(A .2)
The grid -point approximation to the value of a continuous function 1/r(x, t) at the
point (j Sx , nl:i.t) is denoted by cf>' j . Thus,
{, »» _ cf>'j+! - cf>'j_!
2xY'j -
2l:i.x
'
and