## 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

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.