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Waveform relaxation method for fractional differential-algebraic equations

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Abstract

The waveform relaxation method has been successfully applied into solving fractional ordinary differential equations and fractional functional differential equations [11, 5]. In this paper, the waveform relaxation method is further used to solve fractional differential-algebraic equations, which often arise in integrated circuits with new memory materials. We give the iteration scheme of the waveform relaxation method and analyze the convergence of the method under linear and nonlinear conditions for the right-hand of the equations. Numerical examples illustrate the feasibility and efficiency of the method.

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Authors and Affiliations

  1. School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, China

    Xiao-Li Ding

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Yao-Lin Jiang

Authors
  1. Xiao-Li Ding
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  2. Yao-Lin Jiang
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Correspondence to Xiao-Li Ding.

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Ding, XL., Jiang, YL. Waveform relaxation method for fractional differential-algebraic equations. Fract Calc Appl Anal 17, 585–604 (2014). https://doi.org/10.2478/s13540-014-0187-z

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  • DOI: https://doi.org/10.2478/s13540-014-0187-z

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