کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
519785 | 867682 | 2011 | 17 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Numerical approaches to fractional calculus and fractional ordinary differential equation Numerical approaches to fractional calculus and fractional ordinary differential equation](/preview/png/519785.png)
Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for the fractional differential equations are proposed. We use higher order piecewise interpolation polynomial to approximate the fractional integral and fractional derivatives, and use the Simpson method to design a higher order algorithm for the fractional differential equations. Error analyses and stability analyses are also given, and the numerical results show that these constructed numerical approaches are efficient.
Journal: Journal of Computational Physics - Volume 230, Issue 9, 1 May 2011, Pages 3352–3368