Vol. 10, No. 2, 2017

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ISSN: 1944-4184 (e-only)
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Stability analysis for numerical methods applied to an inner ear model

Kimberley Lindenberg, Kees Vuik and Pieter W. J. van Hengel

Vol. 10 (2017), No. 2, 181–196
Abstract

Diependaal, Duifhuis, Hoogstraten and Viergever investigated three time-integration methods to solve a simplified one-dimensional model of the human cochlea. Two of these time-integration methods are dealt with in this paper, namely fourth-order Runge–Kutta and modified Sielecki. The stability of these two methods is examined, both theoretically and experimentally. This leads to the conclusion that in the case of the fourth-order Runge–Kutta method, a bigger time step can be used in comparison to the modified Sielecki method. This corresponds with the conclusion drawn in the article by Diependaal, Duifhuis, Hoogstraten and Viergever.

Keywords
inner ear model, numerical time-integration method, modified Sielecki, fourth-order Runge–Kutta, numerically stable, numerically unstable
Mathematical Subject Classification 2010
Primary: 65L06, 65L07, 65L20, 65M12
Secondary: 65L05, 65L10
Milestones
Received: 9 May 2014
Revised: 14 April 2015
Accepted: 25 March 2016
Published: 10 November 2016

Communicated by Kenneth S. Berenhaut
Authors
Kimberley Lindenberg
Delft University of Technology
Faculty of Electrical Engineering, Mathematics and Computer Science
Department of Applied Mathematical Analysis
2628 CD Delft
The Netherlands INCAS3
9401 HJ Assen
The Netherlands
Kees Vuik
Delft University of Technology
Faculty of Electrical Engineering, Mathematics and Computer Science
Department of Applied Mathematical Analysis
2628 CD Delft
The Netherlands
Pieter W. J. van Hengel
INCAS3
9401 HJ Assen
The Netherlands