1549301742-The_Theory_of_Difference_Schemes__Samarskii

556 Econ0111ical Difference Sche1nes for Multidimensional Proble1ns where un = u(x, tn), ,un+l = u(x, tn+i) and fi is calculated ...

The alternating direction niethod 557 with further reference to the following asymptotic relations: As a final result we obtain ...

558 Economical Difference Schemes for Multidimensional Problems In dealing with non-negative and, generally speaking, non-self-a ...

The alternating direction n1ethocl 559 or Sumn1ing up over k = 0, 1, ... , n and inserting z^0 = 0, we find that ( 43) llzn+lll( ...

560 Economical Difference Schen1es for Multidirnensional Problen1s This 1neans that the second term 0( r^2 ) in the available ex ...

The alternating direction 111ethod 561 where Bex= E - (}ex T Aex and Cex = E + (1-(}ex) T Aex, Cl'= 1, 2. Having multiplied the ...

562 Economical Difference Schen1es for Multidimensional Problems t=tn -. ait +Lu- h~ -Lif--L?f h; l at i 2 12 ~ · t=t n arising ...

The alternating direction inethod 563 Here the operators A 1 and A 2 are supposed to be self-adjoint, positiYe and commuting: A~ ...

564 Econo111ical Difference Sche1nes for Multicliinensional Proble1ns which are i1nmediate implications of the chain of the rela ...

Economical factorized sche1nes^565 Knowing the value y = y1 on the jth layer, it is required to find the value y1 +^1. In prepar ...

566 Economical Difference Schernes for Multidiinensional Problems Especial attention is being paid to the factorized schemes wit ...

Economical factorized schemes 567 The boundary conditions. As one might expect, stability and approx- i1nation take place for t ...

568 Economical Difference Schemes for Multidimensional Problems and the boundary conditions are imposed to be ( 17) that is, w 1 ...

Econmnical factorized sche1nes 569 Sometimes such a passage pennits one to justify the approximation being rp instead of cp near ...

570 Econmnical Difference Schein es for M ultidin1ensional Proble1ns For this, we have occasion to use the two-layer factorized ...

Economical factorized sche1nes 571 can be solved using Gaussian elirnination along the rows for Cl' = l as well as along the col ...

572 Economical Difference Schen1es for Multidhnensional Proble1ns Example 3 As a matter of experience, the intention is to use a ...

Economical factorized schernes 573 In turn, the supplen1entary boundary conditions become ( 30) The second sche1ne: ( 31) with t ...

574 Economical Difference Schen1es for Multidimensional Proble1ns In what follows the weighted scheme (33) y(O) =Yo, Y(r) = U1, ...

Econmnical factorized schernes 575 Knowing the values y1 -l and y1 we do follow the same algorithm for determination of the valu ...