1549301742-The_Theory_of_Difference_Schemes__Samarskii

216 Homogeneous Difference Schemes and taking into account (3), we establish (5) 1 2h X;'i+l (qu - .f) dx. The approximation of ...

Methods for designing difference schen1es 217 Making use of the approximation h J ( qu - .f) dx ~ ( qu - f)o h, 0 we impose the ...

218 Homogeneous Difference Schemes The function u( x) is linearly interpolated on each of the segments [x;_ 1 , x;] and [ x; , X ...

Methods for designing difference schemes 219 scheme ( 12) a;= ~ 7 k(i) di - ~ 7 q(i) (xi - i) (i - xi_ 1 ) di, x; x;+ 1 d; = h\ ...

220 Homogeneous Difference Schemes Let ~ = xn + ()h, 0 < () < 1, that is, xn < ~ < xn+I' n > 0. The balance equat ...

Methods for designing difference schernes 221 Variational difference methods (the Ritz method and the Bubnov-Ga- lerkin method) ...

222 Hmnogeneous Difference Schemes The Ritz inethod proves to be useful in studying the problem (24) (ku')' - q1l = -f(x), 0 < ...

Methods for designing difference schen:1es 223 In light of the properties of the function 7Ji ( x) and its derivatives the matri ...

224 Homogeneous Difference Schemes problems, whose ingredients have no fixed sign and turn out to be non-self- adjoint. In this ...

Methods for designing difference schemes 225 we reduce the syste1n of equations (35) with the inembers &-;- and b.; to (38) ...

226 Homogeneous Difference Sche1nes We introduce the grid wh = {.c; = ih, ·i = 0, 1, ... , N, hN = 1} and approximate on it the ...

Methods for designing difference schemes 227 Adopting those ideas to problem (1), (2), (14) concerning a point heat source, an e ...

228 Homogeneous Difference Schemes The method of the summator identities (the method of approximating an integral identity). A ...

Methods for designing difference schen:1es 229 by means of the relation h J 1 l ( qu - J) dx = 2 h ( qu - f)o + 2 h ( qu - J)i , ...

230 Homogeneous Difference Schemes factors: an error in calculations of pattern functionals, an error in specifying coefficients ...

Stability with respect to coefficients 231 To evaluate a solution of problem (4)-(7) on the basis of (6)-(8), we rely on the est ...

232 Homogeneous Difference Schen1es Stability of the first kind operator equations with respect to coefficients. Here we give t ...

Stability with respect to coefficients 233 via perturbations of I and A. Suppose that the inverse operators A-^1 and JI-^1 exist ...

234 Homogeneous Difference Schemes where D = A-^1!^2 JIA-^1!^2 , and, after this, pass to D^112 y = z: 1 = ( 1 + ex) ( n-^1 z, z ...

Stability with respect to coefficients 235 Theorem Let u be a so~1tion to equation (11) and u be a solution to equation (14), wh ...