Stability Analysis for Solving Ordinary Differential Equation by Finite Difference Method

摘要

A new stability analysis based on the effective condition number is made for the linear algebraic equation Ax=b, which results from the fourth ordinary differential equation, and its bounds are derived. For general cases, the bound of the effective condition number O(h-3.5) is smaller than Cond=O(h-4) with h is the minimal meshspace of the difference grids. The bound of the effective condition number is only O(1) for homogeneous boundary conditions. Namely, these new stability analysis are more valid than previous stability analysis.