Frequency evaluation for exponentially fitted Runge-Kutta methods

By Hans Van De Vyver. 2005

98 citations recorded by the source corpus.

This paper can be seen as a further investigation of the frequency evaluation techniques which are very recently proposed by Ixaru et al. for exponentially fitted multistep algorithms for first-order ordinary differential equations (ODEs). The question answered was how the frequencies should be tuned in order to have a maximal benefit from exponentially fitted methods. In a previous paper, this frequency evaluation algorithm was successfully applied in a direct way to a second-order exponentially fitted Runge-Kutta (EFRK) method of collocation type but such a direct application is impossible for higher-order EFRK methods. To overcome this difficulty we develop an efficient extension of Ixaru's frequency evaluation algorithm for the exponentially fitted RadauIIA method of third order. It is an adaption of Ixaru's algorithm in the sense that instead being applied globally, it is applied stagewise. Numerical experiments illustrate the properties of the developed algorithm.

Subfields: Electrical and Electronic Engineering, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c05679826ea575e018fc33982785458b31b85383

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In Electrical and Electronic Engineering

  1. T. E. Simos
  2. Ibraheem Alolyan
  3. Charalambos Tsitouras
  4. Kenan Mu
  5. Athinoula Kosti
  6. Zacharias A. Anastassi
  7. Jing Ma
  8. Ke Yan

In Numerical Analysis

  1. T. E. Simos
  2. Ibraheem Alolyan
  3. Charalambos Tsitouras
  4. Kenan Mu
  5. Athinoula Kosti
  6. Zacharias A. Anastassi
  7. Ke Yan
  8. Jing Ma

In Statistical and Nonlinear Physics

  1. T. E. Simos
  2. Ibraheem Alolyan

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