1549301742-The_Theory_of_Difference_Schemes__Samarskii

40 Preliminaries

with the coefficients D'k and f3k en1erging frmn (83)-(84). The complete

posing of the problem consists of (83)-(85), which are supplemented with

the initial conditions

(86)

With the right and left differences 6 Vk
vk - Vk-l in the usual sense, the operator

can be factorized by letting

The equality L 1 L 2 1/k = L Yk holds true if

The same procedure works for eliminating /k and bk on the basis of formulae
(83)-(86).