A New Stability Analysis for Solving Biharmonic Equations by Finite Difference Methods.

The paper presents a new stability analysis for the finite difference method (FDM) for biharmonic equations, based on the effective condition number. Upper bounds of the effective condition number and the simplest effective condition number are derived. In general cases, the bound of the effective condition number is O(h-3.5 ), which are smaller than Cond. = O(h-4), where h is the minimal meshspace of the difference grids. Surprisingly, the bounds of the effective condition number are only O(1) for homogeneous boundary conditions. Namely, these new stability analysis are more valid than previous stability analysis. Numerical experiments are provided to verify the stability analysis. [ABSTRACT FROM AUTHOR]