1549301742-The_Theory_of_Difference_Schemes__Samarskii

336 where we find that Difference Schemes with Constant Coefficients au at ' ii.= ui t= t j+1/2 , Hence, 1/; = 0( h^2 +r^2 ) for ...

Asyn1ptotic stability 337 for which I f (μ) I - f (μ1) < o for if P1 < 1 · It is necessary to consider merely the case (1- ...

338 Difference Schemes with Constant Coefficients With this relation in view, it is not difficult to derive the asymptotic expan ...

Asymptotic stability 339 or (^3 +2r>-h) k y)+i k -4Tj k +Tj-i k --^0 , whose solution is sought in the form Ti = qk. Omitting ...

340 Difference Schemes with Constant Coefficients For large j Lhe first harmonic yi ::::::; o: 1 piX 1 clorninates in the soluti ...

Heat conduction equation with several spatial variables 341 In a common setting, let G = G + r be a p-dimensional domain with th ...

342 Difference Schemes with Constant Coefficients The value yj+i on the relevant layer is to be determined by the recursion j = ...

Heat conduction equation with several spatial variables 343 Comparison with the general difference equation (6) A(P) y(P) = B(P, ...

344 Difference Schen1es with Constant Coefficients provided condition (7) holds. With this relation in vrew, we derive the inequ ...

Heat conduction equation with several spatial variables 345 The explicit three-layer scheme. We now turn to the simplest explic ...

346 Difference Schen1es with Constant Coefficients where y = yJ, y = yj-i, r = pr/h^2 and 6. = 4ph-^2 Also, we point out here wi ...

Heat conduction equation with several spatial variables 347 The maximum principle can be applied to any such scheme with weights ...

348 Difference Schen1es with Constant Coefficients We are going to show that the scheme (15) 2 h2 + h2 Yt=LAa(O"aY+(l-O"a)Y)+^1 ...

Heat conduction equation with several spatial variables 349 we address the readers to Chapter 6 and Concluding remarks therein. ...

350 where Difference Schemes with Constant Coefficients 1 ck= (ll 0 , Xk) = J u 0 (x) Xk(x) dx, 0 Granted the grid whT = wh x Wy ...

Shrodinger tin1e-dependent equation 351 The metodology of the rnethod of separation of variables guides the choice ofy(x,t): N-i ...

352 Difference Schemes with Constant Coefficients unstable for any T / h^2 = canst. In contrast to the approved schemes for the ...

Shrodinger time-dependent equation 353 Three-layer schemes. Of special interest is the three-layer scheme with weights (3) Yo= ...

354 Difference Schemes with Constant Coefficients with o:k and /]k arising from the initial conditions y^0 = 'Uo' or Y1 _Yo T y ...

The transfer equation 355 The problem we must solve is the Cauchy problem -oo<x<oo, t > 0' u(x, 0) = 1l 0 (x), under th ...