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A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains

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Abstract

This paper addresses the approximate solution of the fractional Riccati differential equation (FRDE) in large domains. First, the solution interval is divided into a finite number of subintervals. Then, the Legendre–Gauss–Radau points along with the Lagrange interpolation method are employed to approximate the FRDE solution in each subinterval. The method has the advantage of providing the approximate solutions in large intervals. Additionally, the convergence analysis of the numerical algorithm is also provided. Three illustrative examples are given to illustrate the efficiency and applicability of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics, University of Hormozgan, P. O. Box 3995, Bandar Abbas, Iran

    H. Azin & F. Mohammadi

  2. Polytechnic of Porto Department of Electrical Engineering, Institute of Engineering, Rua Dr. Antonio Bernardino de Almeida, Porto, Portugal

    J. A. Tenreiro Machado

Authors
  1. H. Azin
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  2. F. Mohammadi
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  3. J. A. Tenreiro Machado
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Correspondence to F. Mohammadi.

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The authors declared no potential conflicts of interest with respect to the research, authorship, and publication of this paper.

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Communicated by Vasily E. Tarasov.

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Azin, H., Mohammadi, F. & Machado, J.A.T. A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains. Comp. Appl. Math. 38, 96 (2019). https://doi.org/10.1007/s40314-019-0860-2

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  • DOI: https://doi.org/10.1007/s40314-019-0860-2

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