1549301742-The_Theory_of_Difference_Schemes__Samarskii

656 Methods for Solving Grid Equations Also, it seems clear from (9) that where .'h+ 1 is the transition operator from the layer ...

Two-layer iteration schemes 657 proper choices of the para1neter Tk+ 1 and the operators Bk are caused only by the necessity of ...

658 Methods for Solving Grid Equations Theoren1 1 If A is a self-adjoint. opeTatol' (A = A* > 0). then ( 11) 1 B >-TA 2 1 ...

Two-layer iteration schemes On the other hand, it follows from the foregoing that yielding (14) <II A-^1 II ·II Bvk 112 <I ...

660 Methods for Solving Grid Equations The explicit scheme with optimal set of Chebyshev's parameters. In what follows the inte ...

Two-layer iteration sche1nes 661 refers to self-adjoint operators, since any degree of the operator A also is a self-adjoint ope ...

662 Methods for Solving Grid Equations Thus, the well-known Chebyshev polynomial defined by where (24) ]~ 1 (t) =cos (n arccos t ...

Two-layer iteration schemes 663 All this enables us to write clown To Tk = ' 1 +Po tk (29) k= 1,2, ... ,n, thereby completing th ...

664 Methods for Solving Grid Equations The well-established expansion of the function In 1 + x 1 ( 1 1 )^3 1 - x =^2 :r + 3 (1 + ...

Two-layer iteration sche1nes The con di ti on p;' < c is ensured if which is certainly true for ( 36) n > In (1/s) In (1/ ...

666 Methods for Solving Grid Equations In what follows problem (37) will be treated as a model one in the further con1parison of ...

Two-layer iteration sche1nes 667 h SIS SCP 1/10^200 32 1/50^5000 160 1/100^20000 320 Fron1 here it seems clear that much more it ...

668 Methods for Solving Grid Equations operator sk = E - TkA associated with the transition from the ( k - 1 )th iteration to th ...

Two-layer iteration schemes^669 The iteration number k rs recorded along the first column and the quantity of interest is placed ...

670 Methods for Solving Grid Equations upon substituting From such reasoning it seems clear that II sk II = Tk/2 - 1 for tk < ...

Two-layer iteration schenies 671 Re-ordering of iteration para111eters. With regard to scheme (14) one interesting problem aris ...

672 Methods for Solving Grid Equations \!Vhen n = 2P, where p > 0 is an integer, Gn is found by successively applying fonnula ...

Two-layer iteration sche1nes 673 does follow ( 44) in conformity with the values m = nj ,2nj, ... , 2r1-^1 nj. Since 1lj+J = 2"1 ...

674 Methods for Solving Grid Equations collection in a certain sense of t.he paran1eters T 1 , T 2 , ... , T 11 specified by for ...

Two-layer iteration schemes^675 Table 5 k 1 4 5 6 8 9 t:,. k 39.6 4.7 7.4 3.2 1.1 6.7 k 10 16 17 18 24 25 t:,. k 3.2 0.2 3.1 1.5 ...