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]

 那須野 洋 NASUNO Hiroshi
 いわき明星大学科学技術学部 Department of Mechanical Systems and Design Engineering, Iwaki Meisei University

 清水 信行 SHIMIZU Nobuyuki
 いわき明星大学科学技術学部 Department of Mechanical Systems and Design Engineering, Iwaki Meisei University
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Author(s)

 那須野 洋 NASUNO Hiroshi
 いわき明星大学科学技術学部 Department of Mechanical Systems and Design Engineering, Iwaki Meisei University

 清水 信行 SHIMIZU Nobuyuki
 いわき明星大学科学技術学部 Department of Mechanical Systems and Design Engineering, Iwaki Meisei University
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 timestep 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), 37283735, 20061225
The Japan Society of Mechanical Engineers
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