1549301742-The_Theory_of_Difference_Schemes__Samarskii

36 Preliminaries We note in passing that formulae (71 )-(72) just established are very flexible and more convenient for computat ...

Some variants of the elimination method 37 •successive refinement of the coefficients for z = 1, 2, ... , N - 1 with the aid of ...

38 Preliminaries was quite applicable in determination of the periodic solution Yi+N =Yi of problem (61): aiYi-1-CiYi +biYi+l = ...

Some variants of the elimination method 39 Factorization method. At the final stage other ideas are connected with the boundary ...

40 Preliminaries with the coefficients D'k and f3k en1erging frmn (83)-(84). The complete posing of the problem consists of (83) ...

Basic Concepts of the Theory of Difference Schemes In this chapter elementary examples illustrate the basic concepts of the the- ...

42 Basic Concepts of the Theory of Difference Schemes approved rule governing what can happen a vector y = Ax E Y, we say that a ...

Relevant ele1nents of functional analysis 43 it is possible to introduce the operation of multiplication AB of operators A and B ...

44 Basic Concepts of the Theory of Difference Schemes (c) lower semibounded if (6) (Ax, x) > -c, II x 112 for any x EH, where ...

Relevant elements of functional analysis 45 arbitrary linear operator, then A* A and AA* are self-adjoint nonnegative operators: ...

46 Basic Concepts of the Theory of Difference Sche1nes (x, y)A = (y, x)A or (Ax, y) = (x, Ay) = (Ay, x). The axioms of the inner ...

Relevant elernents of functional analysis^47 which confirms the equivalence of (10) and (10'). In the sequel sufficient conditio ...

48 Basic Concepts of the Theory of Difference Schernes for all x. As a matter of fact, (Ax, x) = (A 0 x, x), where A 0 = (A+ A* ...

Relevant elements of functional analysis 49 Lem1na 4 If A is a seH-adjoint positive bounded operator, then the esti- mate is val ...

50 Basic Concepts of the Theory of Difference Schemes If A*= A:'.'.: 0, then all the eigenvalues of A are nonnegative. Any vect ...

Difference approximation of elementary differential operators 51 We would like to discuss the questions raised above in more det ...

52 Basic Concepts of the Theory of Difference Schernes T / N 2 , respectively. After that, we draw the straight lines parallel t ...

Difference approximation of elementary differential operators 53 Example 4. A grid in a two-din1ensional dom.ain. Our final exam ...

54 Basic Concepts of the Theory of Difference Schemes 0 Figure 3. the number N in the case of an equidistant grid. In dealing wi ...

Difference approximation of elementary differential operators 55 space Hh for the grids w h = {xi = ih} on the segment 0 < x ...