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Invariant manifolds of numerical integration schemes applied to stiff systems of singular perturbation type - Part I: RK-methods

by K. Nipp and D. Stoffer

(Report number 1992-14)

Abstract
For implicit RK-methods applied to singularly perturbed systems of ODEs it is shown that the resulting discrete systems preserve the geometric properties of the underlying ODE. As an application of this invariant manifold result sharp bounds on the global error are derived.

Keywords: singular perturbation, attractive invariant manifold, stiff systems, global error, implicit RK-method

@Techreport{NS92_24,
  author = {K. Nipp and D. Stoffer},
  title = {Invariant manifolds of numerical integration schemes applied to stiff systems of singular perturbation type - Part I: RK-methods},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-14.pdf },
  year = {1992}
}

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