A note on impossibility of uniformly non-oscillatory approximation
Ritesh Kumar Dubey
TL;DR
This paper proves that no data-independent three-point finite difference scheme can be uniformly non-oscillatory for scalar hyperbolic initial value problems, regardless of its accuracy.
Contribution
It establishes an impossibility result showing the limitations of three-point schemes in achieving uniform non-oscillatory behavior.
Findings
No data-independent three-point scheme can be uniformly non-oscillatory
The result holds regardless of the scheme's accuracy
Highlights fundamental limitations in finite difference methods
Abstract
In this note we show that it is impossible to have data independent non-oscillatory three point finite difference scheme irrespective of its accuracy for a scalar hyperbolic initial value problem.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Differential Equations and Numerical Methods · Numerical methods in inverse problems