1202.4405 (Lun-Shin Yao)

Convergent Numerical Solutions of Unsteady Problems    [PDF]

Lun-Shin Yao

Von Neumann established that discretized algebraic equations must be
consistent with the differential equations, and must be stable in order to
obtain convergent numerical solutions for the given differential equations. The
"stability" is required to satisfactorily approximate a differential derivative
by its discretized form, such as a finite-difference scheme, in order to
compute in computers. His criterion is the necessary and sufficient condition
only for steady or equilibrium problems. It is also a necessary condition, but
not a sufficient condition for unsteady transient problems; additional care is
required to ensure the accuracy of unsteady solutions.

View original: http://arxiv.org/abs/1202.4405