On the Approximation of Linear Elliptic Differential Equations by Difference Equations with Positive Coefficients
On the Approximation of Linear Elliptic Differential Equations by Difference Equations with Positive Coefficients
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DOI：
10.1002/sapm1952311253
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发表时间：
1952-04
期刊：
影响因子：
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通讯作者：
T. Motzkin;W. Wasow
中科院分区：
文献类型：
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作者：
T. Motzkin;W. Wasow
(2)Lh [u]== 2：~~ 0 c.（x，h）u（x+ mh），其中m.是具有整数分量的n维向量ms，（J= 1，n），并且h是网格长度。在不失一般性的情况下，我们可以假设m.~ mt，对于8~ t，并且mo是零矢量。如果（2）中u（x+ msh）关于点X的形式泰勒展开式产生一个表达式，其开始与L [u]成比例，或者换句话说，如果存在一个函数，则差表达式（2）应称为形式近似，或形式类似于L [u]。（x，h）不恒为零使得X和h恒为零。
(2) Lh [u]== 2:~~ o c.(x, h) u (x+ mh), where m. is an n-dimensional vector with integral components ms,,(J= 1,', n), and h is the mesh length. WIthout loss of generality we can assume that m.~ mt, for 8~ t, and that mo is the zero vector. The difference expreSSIOn (2) shall be called a formal approxtmatwn, or formally analogous to L [u], If the formal Taylor expansions of u (x+ msh) in (2) about the point X produce an expreSSIOn whose begmnmg is proportional to L [uJ, or, in other words, If there is a function}..(x, h) not identically zero such that identically in X and h.