1549301742-The_Theory_of_Difference_Schemes__Samarskii

376 Difference Schemes with Constant Coefficients The identity (37) implies the stability with respect to the initial data in th ...

Difference schen1es for the equation of vibrations of a string 377 In giving a generalized solution of the problern (43) 82 u 82 ...

378 Difference Schen1es with Constant Coefficients with the weight O" = O", is more precise and reproduces much more better the ...

Selected problems The statement of the problem is OU 82 1t 8t - CJx2, O<x<l, t > 0) OU ox (0, t) = μi(t) J 1l ( x, 0) ...

380 Difference Schemes with Constant Coefficients The problem au at u (x, 0) = 0, u(x,t) = 0, x E 8G, t > 0, is approximate ...

Selected problen1s 381 For the three-layer scherne (^11) ,~t t = ()" I ' Yn xx + 1 + ( 1 ()" I _ ()" 2 ) Yn xx + ()" 2 ·yn x ...

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Stability Theory of Difference Schemes In this chapter we study the stability with respect to the initial data and the right-han ...

384 Stability Theory of Difference Schemes the variable t (time) plays a key role and, following established practice, should be ...

Operator-difference schen1es 385 involve in further development the norms II · ll(lh)' II · ll( 2 h)' ... on the space Bh, assum ...

386 Stability Theory of Difference Schemes equation (3) can be recast as (4) Byt+Ay=VJ(t), y(O) = Yo E Bh. We call both equation ...

Operator-difference schemes 387 The canonical form of three-layer schemes. We may attempt the three- layer scheme (2) in the ca ...

388 Stability Theory of Difference Schemes The passage from (6) or (8) to (2) leads to the equation for determining the value Yn ...

Operator-difference sche111es 389 Inequality (12) expresses the property of continuous dependence which is uniform in h and T of ...

390 Stability Theory of Difference Schemes Thus, the three-layer scheme (8) is said to be stable if for any initial data y 0 , y ...

Operator-difference schemes 391 where Tn+l, o =Sn Sn-1 ... S1 So, Tn+l,n+l = E. The operator T,,+ 1 , j is called the transition ...

392 Stability Theory of Difference Schemes To prove this assertion, it suffices to verify that estimate (21) implies estimate ( ...

Operator-difference schemes 393 where y 0 is given. If a scheme with a constant transition operator Sis stable with respect to t ...

394 Stability Theory of Difference Schemes Summarizing, we draw some conclusions which will be needed in the sequel. When the t ...

Operator-difference schemes 395 for all tn nr and that the operators ofsche1ne (4) carry out B~^1 ) into B(2). h. (1) (2) Ah , B ...