542 Difference Methods for Solving Nonlinear EquationsII: "heat group"E = -g(a) vCO 5) - w(f3)
t s s ' w=-kT^8 ,E=E(r1,T), k = x(0.5(P+P(-iJ),0.5(T+Tc-1J)).
After that, Newton's n1ethod of iterations applies equally well to either of
these groups independently. By analogy with the isotennic case the first
group of equations is to be solved with a prescribed temperature, while
the second one needs the assigned values of 7] and v. The essence of the
matter in the last case is that the origin of the heat conduction equation is
stipulated by the available sources of a dyna.1nica.l nature.
The iterations in the first and second groups can be found successively
by the elimination method. Having c01npleted the kth iteration, for which
the condition of termination 116.fi lie = llt - kv
1
lie :S call~ lie is fulfilled,
where Ea > 0 is a prescribed accuracy, there is no doubt that the values t
!.:
and 7] a.re known.
vVith know ledge oft and ~ the mth iteration T is recovered from the
equations of the second group by Newton's method.
The process of the exterior iterations continues to develop prior to the
occurrence of the convergence conditions.
Another way of going further is connected with re-ordering of these
groups in reverse direction or inserting k = 1 and m = 1 in a.II of the
iterations. The separate elimination method may be of assistance in mini-
mizing the total volume of the available infonnation in the storage of high-
performance computers.