536 Difference Methods for Solving Nonlinear Equations- Numerical solution of difference equations by Newton's 1nethod. As
can readily be observed, the system of nonlinear equations capable of spec-
ifying the values vj+l, gj+l and 77j+l on every new layer will be solved
by making several iterations of Newton's method. This can be done by
reducing equations ( 43)-( 44) to the following ones:
~ - 0.5 TVS= 7] + 0.5 TVS,
After that, applying Newton's inethod yields(46)
( 47)
(48)
where
k+l k+l k
6_ 7] - 0.5 T 6_ V = j 2 ,k+l k k+l k k+l k+l- 6 E + Cl!} 6 1) + Cl rJ 6 [/ + CL l/ 6 Us
k = 0, 1, 2, ... ,
a= l/(1 - 1),
k k
f 1 f 2 = 0 for k > 0 ,0 [) 0
j 2 = 1) - 17 + 0 ") T ( Us + Us ) ,k k k k
.3 f = -E + E - g ( o1)(7] - 17),