1549301742-The_Theory_of_Difference_Schemes__Samarskii

596 Economical Difference Sche1nes for Multidhnensional Problems An alternative form of writing includes the intermediate value ...

The su1nn1arized approxiination inethod 597 where fco:(.T:, t), Cl'= 1, 2, ... ,p, are arbitrary functions with the same smo- ot ...

598 Economical Difference Schemes for Multidimensional Problems For example, the weighted scheme suits us for doing so. Here Aa ...

The sum1narized approxilnation method 599 As a matter of experience, the esti1nation of the nearness of a solution of the differ ...

600 Econo1nical Difference Schemes for Multidimensional Problems Thus, the attainable summarized approxi1nation of the additive ...

The sununarizecl approxin:1atio11 rnethocl 601 where t* > 0 is an arbitrary nun1ber. By resolving these equations we obtain y ...

602 Econo1nical Difference Schemes for Multidimensional Problems Example 3 'vVe learn from Ladyzhenskaya (1968) that a solution ...

The sun1n1arized approxin1ation method 603 It is plain to derive for this chain oof the equations the following expressions: 00 ...

604 Econmnical Difference Sche111es for M ultidirnensional Problerns possible at the saine moment only along one direction ;r 1 ...

The sun1marized approxiination n1ethod 605 problem (15) has a unique sufficiently s1nall solution; the intersection of the doma ...

606 Economical Difference Sche1nes for Multidimensional Problems where h:± is the distance between x and x(±la) (h:± <ha)- Th ...

The sumn1arized approximation 1nethod 607 with arbitrary numbers O"": Cl'=l,2, ... ,]J, The describing schen1e is te.nned LOS. I ...

608 Eco1101nical Difference Schernes for Multidimensional Problems et= 1, 2, ... , p. In determining yj+cx/p we inm;t solve the ...

The summarized approxiination 1nethod^609 Further analysis relies on the quantity with omitted superscripts: (27) 0 ( • 1 {ht)j+ ...

610 Economical Difference Schemes for Multidimensional Problems Stability of LOS. The main goal of stability consideration is t ...

The summarized approximation 1nethod where t' = tj'+a/p I llYll C =max xEwh IYI, = 1nax :-i:Ew* h llYll C-y =max XE"fh IYI, =max ...

612 Econmnical Difference Schein.es for Multidimensional Proble1ns containing not only the nodes tj = jr of the grid w 7 , but a ...

The summarized approxim.ation method 613 With regard to problem (32) for w, it will be sensible to rewrite state- ment (32) in t ...

614 Economical Difference Sche1nes for Multidimensional Problems In that case D(P) = l/r and Theorem 3 in Chapter 4, Section 2 s ...

The summarized approximation method 615 Proof Let z(a) = zj+a/p. As usual, we 111ay atternpt a solution z(oJ = Y(a) - uj+a/p of ...