On discretization of the n-dimensional Laplacian

June 12, 2007

Title: A discretization of the n-dimensional Laplacian for a dimension-independent stability limit

Author(s): Anand Kumar

Source: Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 457, No. 2015, (Nov. 8, 2001), pp. 2667-2674.
Abstract:

A discretization of the n-dimensional Laplacian employing all the 3^n points of the finite-difference stencil has been presented. Using this discretization, the stability limit of the heat conduction and the wave equations are found to become dimension-independent \frac{1} {2} and 1, respectively.

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