1549301742-The_Theory_of_Difference_Schemes__Samarskii

96 Basic Concepts of the Theory of Difference Schemes the input data. The two major aims, improved accuracy and better stabil- i ...

Stability of a difference scheme 97 which is approximated on a grid wh = wh +In by a difference problem (20) L1i Yh ='Ph for x E ...

98 Basic Concepts of the Theory of Difference Schemes 2.4 MATHEMATICAL APPARATUS IN THE THEORY OF DIFFERENCE SCHEMES Some diffe ...

Mathe1natical apparatus in the theory of difference sche1nes 99 As in the previous case simila1· formulae of two types (3) (4) a ...

100 Basic Concepts of the Theory of Difference Sche1nes and the inner product on a non-equidistant grid (, ). allow a simpler wr ...

Mathematical apparatus in the theory of difference schemes 101 4) The second Green formula. In the integral calculus the fol- lo ...

102 Basic Concepts of the Theory of Difference Schemes where E > 0 is an arbitrary number, which is sometimes referred to as ...

Mathematical apparatus in the theory of difference schemes 103 1 where Jk = J J (x) uk (x) dx; in so doing 0 1 00 II f 112 = J J ...

104 Basic Concepts of the Theory of Difference Schemes Observe, that the boundary condition at the point x = 0 is automatically ...

Mathe1natical apparatus in the theory of difference schemes 105 We perform simple algebraic calculations and write only the fina ...

106 Basic Concepts of the Theory of Difference Schemes Eigenvalue problems with boundary conditions of the second and third kin ...

Mathematical apparatus in the theory of difference schemes 107 Indeed ' [Ay, v] = (-Yxx, v) + h (^2 2 ) 2 - h Vo Yx,O + h 'UN Yx ...

108 Basic Concepts of the Theory of Difference Schemes and the orthonormal eigenfunctions {μk ( x)}, for which where (28) J.lo = ...

Mathematical apparatus in the theory of difference schemes 109 As can readily be observed, the difference scheme of second-order ...

110 Basic Concepts of the Theory of Difference Sche1nes Difference analogs of the embedding theoren1s. In the estimation of var ...

Mathematical apparatus in the theory of difference schemes 111 Remark 1 Lemma 1 remains valid on an arbitrary non-equidistant gr ...

112 Basic Concepts of the Theory of Difference Schemes Lern1na 3 Any function y( x) defined on the equidistant grid wh = { X; = ...

Mathematical apparatus in the theory of difference schemes 113 The method of energy inequalities. One of the general and very e ...

114 Basic Concepts of the Theory of Difference Schemes This inequality will be aimed at estimating the rate of convergence of sc ...

Mathematical apparatus in the theory of difference schemes 115 scheme (51). We have shown in Section 1.3 that the local approxim ...