1549301742-The_Theory_of_Difference_Schemes__Samarskii

676 Methods for Solving Grid Equations 10.3 THE ALTERNATIVE-TRIANGULAR METHOD Seidel rnethod. As we have mentioned above, impli ...

The alternative-triangular inethod 677 Within these notations, Seidel rnethod can be written as follows: (4) k+l + k. (A +D) y ...

678 Methods for Solving Grid Equations On account of the basic theoren1 proved in Section 1 of the present chapter Seidel method ...

The alternative-triangular n1ethod 679 As shown above, Seidel method is quite applicable for any operator A = A• > 0. However ...

680 Methods for Solving Grid Equations with a known right-hand side Fk. In both cases the matrix B falls within the category of ...

The alternative-triangular method 681 where xk = B^112 wk and C = B-^112 AB-^112. Indeed, because the operator B is self-adjoint ...

682 Methods for Solving Grid Equations Theore1n 2 Let conditions (12) hold. Then an optimal set of parameters { rk} specified b. ...

The alternative-triangular method 683 The alternative triangle 1nethod. Making a substantiated choice of the operator B will be ...

684 Methods for Solving Grid Equations This implies that meaning B = B*. By the same token, It seems clear from the equation giv ...

The alternative-triangular inethod 685 with 0 8 li = ------- l+w8+±w28~' 0 1 (28) l? -=-, 2w where an operator B is specified by ...

686 Methods for Solving Grid Equations when performing current manipulations with the operators B and R: (By,y) = ((E-wR1)(E-wR2 ...

The alternative-triangular 1nethod 687 estimate (18) is true and it suffices to perform n iterations for the valirlit.r of the i ...

688 Methods for Solving Grid Equations Here the composition of the grid is where /1i is its boundary. In that case 0 Ay=-Ay, yEH ...

The alternative-triangular inethod under the inner product structure Ni N2-1 (1t, vL = L L 11i,i2 vi,i2 h1 h2. i1=l i2=l The inn ...

690 Methods for Solving Grid Equations with the supplementary conditions k+l k k k k y = y = 0 on /h, v = y for x E wh, v = p. f ...

The alternative-triangular method 691 k+l giving the values f; and lJ at the centre (£ 1 h 1 , i 2 h 2 ) of the suitably chosen ...

692 Methods for Solving Grid Equations determination of ktl. In so doing the passage from the kth iteration to the (k + l)th ite ...

The alternative-triangular n1ethod 693 Knowing / 1 and / 2 , it remains to find the iteration parameters { r;} with a simple obs ...

694 Methods for Solving Grid Equations Difference schemes for elliptic equations of general form. As we have mentioned above, t ...

The alternative~triangular n1ethod 695 a) An equation of tlie elliptic type with 1nixed derivatives. In that case we are agree t ...