1549301742-The_Theory_of_Difference_Schemes__Samarskii

316 Difference Schemes with Constant Coefficients Summarizing, under condition (39) scheme (16) is stable with respect to the in ...

Heat conduction equation with constant coefficients 317 we find that II OU 112 ~ ~ II OU 112 = ( OU ) ot + 2 ot ox f ' ot · To m ...

318 Difference Schemes with Constant Coefficients and taking into consideration the trivial identities y 2 1 ( y A + y ) - 2 1 T ...

Heat conduction equation with constant coefficients one succeeds in showing that J > 0 for(}> () 0. Because of (45), l= ll ...

320 Difference Schemes with Constant Coefficients Substitution of ( 49) into ( 48) gives Summing over/= 0, 1, ... ,j and keeping ...

Heat conduction equation with constant coefficients^321 The third kind boundary conditions. The first kind boundary conditions ...

322 Difference Schernes with Constant Coefficients It is straightforward to verify that at the point x = 1 the boundary condi- t ...

Heat conduction equation with constant coefficients 323 approximation happens to be the same as we obtained for the boundary- va ...

324 Difference Sche1nes with Constant Coefficients But it is absolutely unstable: this scheme becon1es unstable for any way of t ...

Heat conduction equation with constant coefficients 325 Keeping T = ah (1 + O(h)) with CL = const we draw the conclusion that sc ...

326 Difference Schemes with Constant Coefficients Omitting the terms O(h^2 ) in (65) and involving the equation u = u" + f insig ...

Heat conduction equation with constant coefficients 327 These boundary conditions generate an approximation of O(h^2 + T) for an ...

328 Difference Schemes with Constant Coefficients the minimal expenses of execution time. A number of operations may be minimize ...

Asymptotic stability 329 This stage of the process refers to the regular behavior. When the so- lution of a difference scheme fo ...

330 Difference Schemes with Constant Coefficients Asymptotic stability. Let us describe rathel' mild conditions under which the ...

Asymptotic stability 331 for the symmetric scheme with (} = ~ under the constraint T < 2 ( c5 b. )-^112. We bring together th ...

332 Difference Schemes with Constant Coefficients with the asymptotic expansion f3 = ~ T 62 - i T^2 63 + · · · = 0( T). It is ev ...

Asymptotic stability 333 and the stability condition T < h^2 /2 also irnplies that T < 2 (D + 6.)-^1. In the case of a sym ...

334 Difference Schemes with Constant Coefficients where XN-i(xi) =sin 7r(N - 1) X; =sin 7r(N - 1) ih =sin 7r(l - h) i = (-1)'-^1 ...

Asymptotic stability^335 The usual trick amounts to eliminating yJ+^1 /^2 from (8) so as to reduce the governing difference equa ...