Asymptotic expansions and approximations for the Caputo derivative

被引：5

作者：

Dimitrov, Yuri ^{[1
]}

Miryanov, Radan ^{[2
]}

Todorov, Venelin ^{[3
,4
]}

机构：

[1] Univ Forestry, Dept Math & Phys, Sofia 1756, Bulgaria

[2] Univ Econ, Dept Stat & Appl Math, Varna 9002, Bulgaria

[3] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev Str,Bl 8, BU-1113 Sofia, Bulgaria

[4] Bulgarian Acad Sci, Inst Informat & Commun Technol, Acad G Bonchev Str,Bl 25A, BU-1113 Sofia, Bulgaria

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 04期

关键词：

Binomial coefficient; Asymptotic expansion; Approximation of the Caputo derivative; Numerical solution; FRACTIONAL DIFFUSION EQUATION; DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; CALCULUS; SCHEME;

D O I：

10.1007/s40314-018-0641-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we use the asymptotic expansions of the binomial coefficients and the weights of the L1 approximation to obtain approximations of order and second-order approximations of the Caputo derivative by modifying the weights of the shifted Grunwald-Letnikov difference approximation and the L1 approximation of the Caputo derivative. A modification of the shifted Grunwald-Letnikov approximation is obtained which allows second-order numerical solutions of fractional differential equations with arbitrary values of the solutions and their first derivatives at the initial point.

引用

页码：5476 / 5499

页数：24

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