HOW TO APPROXIMATE THE FRACTIONAL DERIVATIVE OF ORDER 1 < α ≤ 2

被引：67

作者：

Sousa, Ercilia ^{[1
]}

机构：

[1] Univ Coimbra, Dept Math, CMUC, P-3001454 Coimbra, Portugal

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 04期

关键词：

Diffusion; fractional derivative; finite differences; consistency; accuracy; ADVECTION-DISPERSION EQUATION; FINITE-DIFFERENCE APPROXIMATIONS; DIFFUSION-EQUATIONS; SOLUTE TRANSPORT;

D O I：

10.1142/S0218127412500757

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The fractional derivative of order alpha, with 1 < alpha <= 2 appears in several diffusion problems used in physical and engineering applications. Therefore to obtain highly accurate approximations for this derivative is of great importance. Here, we describe and compare different numerical approximations for the fractional derivative of order 1 < alpha <= 2. These approximations arise mainly from the Grunwald-Letnikov definition and the Caputo definition and they are consistent of order one and two. In the end some numerical examples are given, to compare their performance.

引用

页数：13

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