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Accurancy barriers of three time level difference schemes for hyperbolic equations

by R. Jeltsch and J. H. Smit

(Report number 1991-04)

Abstract
A basic assumption for the interior scheme when solving hyperbolic mixed initial boundary value problems is that it satisfies the von Neumann stability condition. Here we show that this condition limits the order of accuracy a scheme with a given difference stencil can have. The proofs use order stars.

Keywords: difference schemes, hyperbolic equations, initial boundary value problem, mixed initial value problems, Neumann stability, accuracy barriers, order stars

@Techreport{JS91_4,
  author = {R. Jeltsch and J. H. Smit},
  title = {Accurancy barriers of three time level difference schemes for hyperbolic equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1991-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1991/1991-04.pdf },
  year = {1991}
}

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