1549301742-The_Theory_of_Difference_Schemes__Samarskii

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Contents Preface 111 1 Prelin1inaries 1 1.1 Difference equations l 1.2 So1ne variants of the eliinination n1ethocl ;34 2 Basic c ...

xvi Contents 3.2 Conservative schemes 147 3.3 Convergence and accuracy of homogeneous conservative schemes 159 3.4 Hornogeneous ...

Contents xvii 6.3 Classes of stable three-layer schemes 428 7 Ho111ogeneous difference sche111es for tin1e-dependent equations o ...

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Preliminaries Conte1nporary methods for solving problems of n1athen1atical physics are gaining increasing popularity. They are b ...

2 Preli1ninaries Most of the well-developed methods available for solving such a system falls within the categories of direct or ...

Difference equations 3 Lu = u' known from differential calculus. The same procedure works for the second, the third and other di ...

4 Preliminaries and offer below some of its approximations with new notations Vi= v(xi), Vi+l = v(xi+d and x,:+1 = ;ri + h, wher ...

Difference equations the sum of which gives Ui+l - 2 Ui + Ui-l h2 5 Neglecting 0( h^2 ) we derive rough expressions for u" withi ...

6 Preliminaries In the general case b = bi, a = ai and c = Ci, that is, we deal with known functions of the argument i. If bi -: ...

Difference equations^7 The second-order difference equations. The Cauchy problem. Bounda- ry-value problems. The second-order d ...

8 Preliminaries For the second-order difference equations capable of describing the basic mathematical-physics problems, boundar ...

Difference equations 9 In the case of boundary conditions of the second or third kinds its order is N + 1, while for the system ...

10 Preliminaries under agreement (10). By going through the matter chronologically the forward elimination path for finding o:i, ...

Difference equations general case: (--+) B; CY i+l = C'; - CY; A; ' A; {3; + F; C'; - CY; A; ' (~) Y i = CYi+1 Yi+1 + f3;+1 , 11 ...

12 Prelhninaries as well as ID'i+1I < 1 are ensured by ICl'il < 1. The assumption 10' 11 = lx 11 < 1 implies ICl'il < ...

Difference equations 13 The left elimination method. The counter elimination method. Still using the framework of the right eli ...

14 Preliminaries node i = i 0 , 0 < i 0 < N, and to compute the coefficients a; and /]; for 0 < i < i 0 + 1 accordin ...

Difference equations 15 Theorem 1 (The maximum principle). Let tlie conditions (22) A;> 0, B; > 0, D; = Ci - Ai - Bi > ...