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

共 35 条

[1] A new difference scheme for the time fractional diffusion equation
Alikhanov, Anatoly A.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 280 : 424 - 438
[2] New Operational Matrices for Solving Fractional Differential Equations on the Half-Line
Bhrawy, Ali H.
Taha, Taha M.
Alzahrani, Ebrahim O.
Baleanu, Dumitru
Alzahrani, Abdulrahim A.
[J]. PLOS ONE, 2015, 10 (05):
[3] FOURTH ORDER ACCURATE SCHEME FOR THE SPACE FRACTIONAL DIFFUSION EQUATIONS
Chen, Minghua
Deng, Weihua
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (03) : 1418 - 1438
[4] ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF LINEAR MULTI-ORDER FRACTIONAL DIFFERENTIAL SYSTEMS
Diethelm, Kai
Siegmund, Stefan
Tuan, H. T.
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2017, 20 (05) : 1165 - 1195
[5] Dimitrov Dim14 Yuri, 2014, J. Fract. Calc. Appl., V5
[6] Dimitrov Y., 2018, J. Fract. Calc. Appl, V9, P35, DOI [https://doi.org/10.48550/arXiv.1605.06912, DOI 10.48550/ARXIV.1605.06912]
[7] Dimitrov Y., 2017, EC COMPUT SCI, V4, P23
[8] Dimitrov Y., 2016, J FRACT CALC APPL, V7, P175
[9] High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions
Ding, Hengfei
Li, Changpin
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2017, 71 (02) : 759 - 784
[10] HIGH-ORDER ALGORITHMS FOR RIESZ DERIVATIVE AND THEIR APPLICATIONS (III)
Ding, Hengfei
Li, Changpin
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (01) : 19 - 55

← 1 2 3 4 →