Modified 5-point fractional formula with Richardson extrapolation

被引：7

作者：

Batiha, Iqbal M. ^{[1
,2
]}

Alshorm, Shameseddin ^{[1
]}

Jebril, Iqbal ^{[1
]}

Zraiqat, Amjed ^{[1
]}

Momani, Zaid ^{[3
]}

Momani, Shaher ^{[2
,4
]}

机构：

[1] Al Zaytoonah Univ Jordan, Dept Math, Amman 11733, Jordan

[2] Ajman Univ, Nonlinear Dynam Res Ctr NDRC, Ajman, U Arab Emirates

[3] Univ Texas Arlington, Dept Civil Engn, Box 19308,428 Nedderman Hall, Arlington, TX 76019 USA

[4] Univ Jordan, Dept Math, Amman 11942, Jordan

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 04期

关键词：

Richardson extrapolation; Riemann-Liouville fractional derivative and integral; Lagrange interpolating polynomial; Caputo derivative;

D O I：

10.3934/math.2023480

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

引用

页码：9520 / 9534

页数：15

共 24 条

[1]

Aho Alfred V, 1974, Addison-Wesley Series in Computer Science and Information Processing, P5

[2]

Aitken A. C., 1932, Proc. Edinburgh Math. Soc., V3, P56

[3] Numerical solutions for linear fractional differential equations of order 1 < alpha < 2 using finite difference method (FFDM) [J].

Albadarneh, Ramzi B. ;

Batiha, Iqbal M. ;

Zurigat, Mohammad .

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2016, 16 (01) :103-111

[4]

Albadarneh RB., 2021, INT J EL COMP ENG SY, V11, P5367, DOI DOI 10.11591/IJECE.V11I6.PP5367-5378

[5]

Allgower E. L., 1990, Numerical continuation methods

[6]

[Anonymous], 1984, Computer Science and Applied Mathematics

[7]

[Anonymous], 2005, Numerical Analysis

[8]

[Anonymous], 1992, Numerical Analysis of Partial Differential Equations

[9]

Argyros I.K., 1993, The Theory and Application of Iteration Methods, DOI DOI 10.1201/9780203719169

[10] (N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations [J].

Arshad, Muhammad ;

Lu, Dianchen ;

Wang, Jun .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 48 :509-519

← 1 2 3 →