2012/02/20 by Lun-Shin Yao, Yao, Lun-Shin
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1202.4405
openalex publication_date 2012/02/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.