ベキ時間を用いた分数階微分方程式の数値積分法(機械力学,計測,自動制御)

概要

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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.
社団法人日本機械学会の論文
2006-12-25