ベキ時間を用いた分数階微分方程式の数値積分法  [in Japanese] Numerical Integration Algorithm for Fractional Differential Equation by means of Power Time  [in Japanese]

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Author(s)

Abstract

This paper is concerned with the development of an efficient algorithm for the numerical solution of the fractional differential equation (FDE). The numerical integration of the FDE requires significant computational cost, because the fractional convolution integral included in the fractional derivative, requires O(N^2) operations for N points calculation. The kernel of the fractional integral has singularity and consequently excessive small time-step near the singularity is needed to secure the high precision in the numerical calculation. This difficulty is solved by means of a new computational procedure for fractional derivative by introducing the variable trasformation from the physical time to the power time which is newly defined in this paper. The proposed algorithm is used to solved the nonlinear FDE. Computational results are compared with those by the former method (Nasuno and Shimizu, JSME (C), 2006). The proposed method shows remarkably higher performance than the former one.

Journal

  • Transactions of the Japan Society of Mechanical Engineers C

    Transactions of the Japan Society of Mechanical Engineers C 73(724), 3728-3735, 2006-12-25

    The Japan Society of Mechanical Engineers

References:  21

Cited by:  1

Codes

  • NII Article ID (NAID)
    110006153460
  • NII NACSIS-CAT ID (NCID)
    AN00187463
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • ISSN
    03875024
  • NDL Article ID
    8628336
  • NDL Source Classification
    ZN11(科学技術--機械工学・工業)
  • NDL Call No.
    Z16-1056
  • Data Source
    CJP  CJPref  NDL  NII-ELS 
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