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But the loss may be more than offset by stronger demand for gas turbines, wind generators, and equipment to make power grids function more efficiently.
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A function (varphi ^{h} ( x ) ) defined on (mathbb{R}_{hn}^) will be called a grid function.
A function defined on (mathbb{R}_{h}^{n-1}) will be called a grid function.
In particular, the backward difference quotients of each grid function { u i j ( k ) } are bounded.
It will be values of the grid function φ 0 in the boundary condition (13).
For any grid function (uinmathcal{V}_{h}), we introduce the notations below.
For any grid function (uinmathcal{S}_{h}), |u|leqfrac{L}{sqrt{6}}|delta_{x} u|.
Lemma 2. Let {u ij } and {v ij } be two grid functions defined at the mesh points (x i, y j ) of the grid R h ∪ ∂R h, i = 0,..., N + 1, j = 0,..., M + 1 such that, at the point (x i, y j ) of ∂R h and t > 0, the grid function {u ij } is equal to the prescribed function U1(x i, y j, t) and the grid function {v ij } is equal to the null function, respectively.
(3)This formula defines a (2pi h^{-1} -periodic smooth^{-1} -periodice continuous argument ξ wh^{-1} -periodic x ) ) ismoothpidly decreasing grid function.
we find values of the grid function φ k m for m = 1, N − 1 on the sides of Γ 1 h parallel to OX axis.
Therefore, from the stability of problem (18), we get the convergence of the grid function to { U ( x k, y m ) } ([9], p.30, Theorem 2.5).
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