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Reducibility and contractivity of Runge-Kutta methods revisited

by G. Dahlquist and R. Jeltsch

(Report number 2006-03)

Abstract
The exact relation between a Cooper like reducibility concept and the reducibilities introduced by Hausdorfer, Spijker and by Dahlquist and Jeltsch is given. A shifted Runge-Kutta scheme and a transplanted differential equation is introduced in such a fashion that the input/output relation remains unchanged under these transformations. This gives a technique to prove stability and contractivity results. This is demonstrated on the example of contractivity disks.

Keywords: Reducibility, irreducibility of Runge Kutta methods, contractivity, monotonicity, nonlinear stability, algebraic stability

@Techreport{DJ06_352,
  author = {G. Dahlquist and R. Jeltsch},
  title = {Reducibility and contractivity of Runge-Kutta methods revisited},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2006-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2006/2006-03.pdf },
  year = {2006}
}

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