
213
Chapter 5
Stability analyses
5.1 INTRODUCTION
A numerical method must have a stable behaviour to simulate time-
dependent problems. Thus, a rigorous stability analysis of a numerical
method is essential before it is relied upon to solve time-dependent prob-
lems; in particular, it is vital for strong form- based methods. This aspect
of a meshless method is elaborated in this chapter by studying the stability
characteristics of meshless RDQ method. This is accomplished by analyz-
ing the locations of zeros or roots of its characteristic polynomials with
respect to the unit circle in the complex plane, by discretizing the domain
with either u