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標題: 在圓盤上討論一些離散化的
Some Discrete Green Identities on a Disk
作者: 黃必錦
Huang, Pi-Chin
關鍵字: Green identities
discrete Laplacian operator
discrete gradient
出版社: 應用數學系
摘要: A great deal of studies of applied math questions has been made on natural science or engineering with the domain of two- dimensional or three- dimensional un-rectangular coordinates system, such as disk, sphere, spheroid, cylinder, even oval and ellipsoid. Let us take the domain of the function as if it is on a unit disk. Meanwhile we transfer Cartesian coordinates system into the polar coordinates system. Furthermore, we discretize the Green identities which are on polar coordinates system by another form of the discrete Laplican operator, then we obtain some discrete formulae and find that the scheme does not need to define the value of the mesh function at pole. In this study, for me, the main stress falls on how to let us avoid singular point(pole) and turn to request the discrete Green identities. Finally, we expect that our discrete formulae are useful for the stability of numerical scheme of the boundary condition problems for elliptic partial differential equation.
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