The sumn1arized approximation 1nethod 607
with arbitrary numbers O"":Cl'=l,2, ... ,]J,
The describing schen1e is te.nned LOS. In what follows we confine. ourselves
to the applications of purely in1plicit LOS 's with O" o: = 1:(21)0: = 1,2, ... ,]J,
In preparation for this, the preceeding is put together with the boundary
condition(22) for XE/ho:> , j=0,l, ... ,J 0 ,
Cl'=l,2, ... ,p,
and the initial condition(23) y( X, Q) = Ua ( X).
As we will see a little later, the right-hand side i.pi,+"!P 0: and the boundary
value yi+afpl,h,o can be expressed through the functions f,..(x, t) and p(x, t)
taken at arbitrary moments t:, and t:• from the segment [tj, tj + 1 ], so that
~+o:/p = fo:(x, t:) and pi+a/p = p(:r, t:;), thereby retaining the accuracy
order. For the sake of definiteness, we accept(^1) re, ni+o:/p -- f a (x ' t ;+0.5 · ) ' f.-l J+a/p --p (· x, t i+o:/p' ) Cl'=l,2, ... ,p,
by regarding yi to the known values. The value ji+l can be found on
every new layer from (21)-(22) by successive solution of p equations of the
form (21) with the boundary conditions (22) in a step-by-step fashion for