A finite difference scheme for Caputo-Fabrizio fractional differential equations
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摘要In this work, we consider a new fractional derivative with nonsingular kernel introduced by Caputo-Fabrizio (CF) and propose a finite difference method for computing the CF fractional derivatives. Based on an iterative technique, we can reduce the computational complexity from O(J(2)N) to O(JN), and the corresponding storage will be cut down from O(JN) to O (N), which makes the computation much more efficient. Besides, by adopting piece-wise Lagrange polynomials of degrees 1, 2, and 3, we derive the second, third, and fourth order discretization formulas respectively. The error analysis and numerical experiments are carefully provided for the validation of the accuracy and efficiency of the presented method.
著者Guo X, Li YT, Zeng TY
期刊名稱International Journal of Numerical Analysis and Modeling
出版年份2020
卷號17
期次2
出版社Institute for Scientific Computing and Information, University of Alberta
頁次195 - 211
國際標準期刊號1705-5105
語言英式英語
關鍵詞Caputo-Fabrizio derivative, fractional differential equations, higher order scheme
Web of Science 學科類別Mathematics, Applied;Mathematics;Mathematics

上次更新時間 2020-22-09 於 01:10