Convergent Numerical Solutions of Unsteady Problems

Details Convergent Numerical Solutions of Unsteady Problems Convergent Numerical Solutions of Unsteady Problems

2012-02-20

arxiv.org/abs/1202.4405v2

Mathematics

Numerical Analysis

8 pages, 2 figures

Scientific paper

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.

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