1549301742-The_Theory_of_Difference_Schemes__Samarskii

The summarized approxiination 1nethod^609

Further analysis relies on the quantity with omitted superscripts:

(27)

0 ( • 1 {ht)j+l/2

1jJ CY = L CK 1l + Jc, - p at.

A simple observation that

in the case where

serves as a basis for the representation of 1/J~ ~ = ?jJj+cr/p c> as a sun1

where

Fron1 the very definition of A,,. and 'Po it follows that

1/J: = O(h! + r) at the regular nodes,

1/J: = 0( l) at the irregular nodes.

Thus, we inight have

p p

·1/J = L ?/Ja = L 1/J: = O(r+ lhl")

a=l a=l

at the regular nodes, that is, LOS in question generates a summarized
approximation of 0( T + lh 12 ) at the regular nodes of the grid w h, while
1/^1 = 0( 1) at the irregular nodes.