A note on impossibility of uniformly non-oscillatory approximation
arXiv:1505.06977
Originality Incremental advance
AI Analysis
Establishes a fundamental limitation for finite difference schemes in hyperbolic PDEs, relevant to numerical analysts.
The authors prove that no data-independent three-point finite difference scheme can be uniformly non-oscillatory for scalar hyperbolic problems, regardless of accuracy.
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.