Numerical approaches to fractional calculus and fractional ordinary differential equation

作者：Li, Changpin^*; Chen, An; Ye, Junjie

来源：Journal of Computational Physics, 2011, 230(9): 3352-3368.

DOI：10.1016/j.jcp.2011.01.030

• Numerical approach
• Fractional calculus
• Fractional differential equations
• Piecewise interpolation
• Simpson method

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.

• 出版日期2011-5-1
• 单位上海大学