1549301742-The_Theory_of_Difference_Schemes__Samarskii

436 Stability Theory of Difference Schemes Theorem 3 Let the conditions of Theorem 1 be satisfied. Then scheme ( 1) is stable wi ...

Classes of stable three-layer sche1nes 437 Lemma 2 If y(O) = y( r) = 0, then t (42) II y(t) 112 +II y(t + r) 112 < 4t LT II Y ...

438 Stability Theory of Differe11ce Sche1nes Theore1n 5 Let A = A* > 0, R = R* > 0 and B = B* > 0, A and R be constant ...

Classes of stable three-layer schemes 439 We modify the expression in the brackets on the right-hand side of identity (18) by a ...

440 Stability Theory of Difference Schemes Identity (53) yields (57) 2T (By~) yt) + J(t + T) < ( 1 + ( 2 +cc) c^3 T) J(t) + 2 ...

Classes of stable three-layer schemes 441 Weighted schemes. In practice the reader frequently encountered the weighted schemes ...

442 Stability Theory of Difference Schemes where Proof In what follows we distinguish two separate tasks. ~ lj Stabili!J with re ...

Classes of stable three-layer schemes 443 Substituting (75) into the right-hand side of the inequality n II Yn+l II < L T II ...

444 Stability Theory of Difference Schemes while the estimate of the form (61) is valid for Examples. It seems worthwhile givin ...

Classes of stable three-layer sche1nes 445 Comparison of this equation with (79) gives u = l/h^2 > II A 11/4, that is, the Du ...

446 (82) Stability Theory of Difference Schemes \!Ve now consider the scheme with a skew-syn1111etric operator A: yo + Ay = 0, t ...

Classes of stable three-layer schemes 447 0 Let H = SL h be the space of all complex functions defined on the grid wh and vanish ...

448 Stability Theory of Difference Schemes associated with the transfer equation which is stable for T / h < 1. Observe that ...

Classes of stable three-layer schernes^449 assuming that (85) A(t)=A(t)>O, D(t)=D(t)>O, B(t)>O, (86) A(t) and D(t) are ...

450 Stability Theory of Difference Schemes Proof To make our exposition more transparent, it is convenient to deal with J = ~ 11 ...

Classes of stable three-layer schern.es 451 Applying now the inequality ab < 8a^2 + 62 /( 48) yields (94) Assuming the second ...

452 Stability Theory of Difference Schernes Since D > 0 and the space H is finite-din1ensional, D > liE and the inverse op ...

Classes of stable three-layer schemes 453 In order to understand the nature of this a little better, we take for granted that A ...

454 Stability Theory of Difference Schemes Theorem 10 If conditions (87) and (102) are satisfied, then for scheme (101) a priori ...

Classes of stable three-layer sche111es 455 (108) (109) In studying the canonical form of two-layer and three-layer schemes (E+r ...