1549301742-The_Theory_of_Difference_Schemes__Samarskii

156 Homogeneous Difference Schemes In practice it is convenient to employ more simpler formulae for de- termination of a, d and ...

Conservative schemes 157 convenience in analysis, it is supposed that F[,f(s)] is a linear nonnegative functional such that (1) ...

158 Homogeneous Difference Schemes Comparision of the resulting expansions with (18) permits us to assign the values (21) A[l] = ...

Conservative schemes 159 provided conditions (20)-(21) hold. In what follows we deal everywhere with the primary family of ho- r ...

160 Homogeneous Difference Schemes is the error of approximation of equation (1) by the difference scheme (2) on the solution u ...

Convergence and accuracy of homogeneous conservative schemes 161 This can be done with the aid of the balance equation upon inte ...

162 Homogeneous Difference Schemes helps motivate what is clone with 1/J; = (qi 1l; - d, Hi) + ( <p; - Ji) + 0( h^2 ) = O(h^2 ...

Convergence and accuracy of hon1ogeneous conservative schemes 163 It seems worthwhile to focus the reader's attention on the bes ...

164 Homogeneous Difference Schemes It follows from the foregoing that (10) 17; = O(h^2 ) 1/J; = O(h^2 ) 0 1/;~ = O(h) 1/J; = O(h ...

Convergence and accuracy of homogeneous conservative schemes 165 where 1/;(x) is the error of approximation having the form (6): ...

166 Ho1nogeneous Difference Sche1nes As far as Ai < AN, the preceding decomposition implies that The difference t;; = v; - w; ...

Convergence and accuracy of homogeneous conservative schemes 167 Theorem 1 The accuracy of any scheme (2) with coefficients (16) ...

168 Homogeneous Difference Schemes 3.4 HOMOGENEOUS DIFFERENCE SCHEMES ON NON-EQUIDISTANT GRIDS Schemes on non-equidistant grids ...

Homogeneous difference sche1nes on non-equidistant grids 169 lead to the difference scheme 0 0 (2) - a-o z Yi -h Yi-1] - di Yi = ...

170 Homogeneous Difference Schemes When the available functions k(x), q(x) and J(x) happen to be of the class QC^0 l[o, 1] and t ...

Homogeneous difference schemes on non-equidistant grids 171 where 1/;(x) = (aux)x - du+ <p(x) is the error of approximation. ...

172 Homogeneous Difference Schemes The order of accuracy on non-equidistant grids. As before, the inner products are defined by ...

Ho1nogeneous difference schemes on non-equidistant grids 173 which are always valid, we follow the same procedures in the accura ...

174 Homogeneous Difference Sche1nes A greater gain in accuracy on a sequence of grids. The Runge method. In a common setting we ...

Hom.ogeneous difference schemes on non-equidistant grids 175 this approach a little better, we consider the simplest case, provi ...