1549301742-The_Theory_of_Difference_Schemes__Samarskii

Stability and convergence of the Dirichlet difference problem 269

In this case the function D( x) takes on the value

D(x) = A(x) -

~EP att' (x)

Etfo

B(J:,~)

= A(J:) - [ ~ B(x, ~) - B(x, ~ 0 )]

EEPatt'(x)

srnce A( x) = L B( x, 0 for the Laplace equation. This provides

EEPatt'(x)

support for the view that

D(x) = B(x, x(+l,,)) > 0.

If a node x is near-boundary not only with respect to .r °', but also in
other directions, then sum ( 12) contains no other terms for~ = ~ 1 , ~ 2 , ..• , ~ k,
so that

Let x E w 7, be a near-boundary and irregular node only in some di-

rection Xa and ~ 0 = x(+i") E /h, x(-!") E wh. From the equation

where

p

A~w+ L A(Jw=-<p*(x),

(3= l

(3 ;t °'

A(J y = Yx13:r13'