Modified Three-Point Fractional Formulas with Richardson Extrapolation

Iqbal M. Batiha; Shameseddin Alshorm; Adel Ouannas; Shaher Momani; Osama Y. Ababneh; Meaad Albdareen

doi:10.3390/math10193489

Modified Three-Point Fractional Formulas with Richardson Extrapolation

Iqbal M. Batiha
, Shameseddin Alshorm
, Adel Ouannas
, Shaher Momani
, Osama Y. Ababneh
, Meaad Albdareen

Nonlinear Dynamic Research Centre (NDRC)

Irbid National University
Al al-Bayt University
University of Oum El Bouaghi
University of Jordan
Zarqa University

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of (Formula presented.) numerically. 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.

Original language	English
Article number	3489
Journal	Mathematics
Volume	10
Issue number	19
DOIs	https://doi.org/10.3390/math10193489
State	Published - Oct 2022

Keywords

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

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10.3390/math10193489

Cite this

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title = "Modified Three-Point Fractional Formulas with Richardson Extrapolation",

abstract = "In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function{\textquoteright}s behavior according to different fractional-order values of (Formula presented.) numerically. 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.",

keywords = "Caputo derivative, Lagrange interpolating polynomial, Richardson extrapolation, Riemann–Liouville fractional derivative and integral",

author = "Batiha, \{Iqbal M.\} and Shameseddin Alshorm and Adel Ouannas and Shaher Momani and Ababneh, \{Osama Y.\} and Meaad Albdareen",

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doi = "10.3390/math10193489",

language = "English",

volume = "10",

journal = "Mathematics",

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T1 - Modified Three-Point Fractional Formulas with Richardson Extrapolation

AU - Batiha, Iqbal M.

AU - Alshorm, Shameseddin

AU - Ouannas, Adel

AU - Momani, Shaher

AU - Ababneh, Osama Y.

AU - Albdareen, Meaad

PY - 2022/10

Y1 - 2022/10

N2 - In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of (Formula presented.) numerically. 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.

AB - In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of (Formula presented.) numerically. 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.

KW - Caputo derivative

KW - Lagrange interpolating polynomial

KW - Richardson extrapolation

KW - Riemann–Liouville fractional derivative and integral

UR - https://www.scopus.com/pages/publications/85139798947

U2 - 10.3390/math10193489

DO - 10.3390/math10193489

M3 - Article

AN - SCOPUS:85139798947

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 19

M1 - 3489

ER -

Modified Three-Point Fractional Formulas with Richardson Extrapolation

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Keywords

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