Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

Zakieh Avazzadeh; Omid Nikan; José Tenreiro Machado; Mohammad Navaz Rasoulizadeh

doi:10.1186/s13662-022-03720-w

Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

Zakieh Avazzadeh
, Omid Nikan^*
, José Tenreiro Machado
, Mohammad Navaz Rasoulizadeh

^*Corresponding author for this work

Department of Applied Mathematics

Iran University of Science and Technology
Polytechnic of Porto
Velayat University

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

8 Citations (Scopus)

Abstract

This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.

Original language	English
Article number	48
Journal	Advances in Continuous and Discrete Models
Volume	2022
Issue number	1
DOIs	https://doi.org/10.1186/s13662-022-03720-w
Publication status	Published - Dec 2022

Keywords

Caputo fractional derivative
Finite difference
Local meshless method
RBF
Stability
Time-fractional Sobolev equation

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10.1186/s13662-022-03720-w

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title = "Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks",

abstract = "This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.",

keywords = "Caputo fractional derivative, Finite difference, Local meshless method, RBF, Stability, Time-fractional Sobolev equation",

author = "Zakieh Avazzadeh and Omid Nikan and \{Tenreiro Machado\}, Jos{\'e} and Rasoulizadeh, \{Mohammad Navaz\}",

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year = "2022",

month = dec,

doi = "10.1186/s13662-022-03720-w",

language = "English",

volume = "2022",

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T1 - Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

AU - Avazzadeh, Zakieh

AU - Nikan, Omid

AU - Tenreiro Machado, José

AU - Rasoulizadeh, Mohammad Navaz

PY - 2022/12

Y1 - 2022/12

N2 - This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.

AB - This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.

KW - Caputo fractional derivative

KW - Finite difference

KW - Local meshless method

KW - RBF

KW - Stability

KW - Time-fractional Sobolev equation

UR - https://www.scopus.com/pages/publications/85133010993

U2 - 10.1186/s13662-022-03720-w

DO - 10.1186/s13662-022-03720-w

M3 - Article

AN - SCOPUS:85133010993

SN - 2731-4235

VL - 2022

JO - Advances in Continuous and Discrete Models

JF - Advances in Continuous and Discrete Models

IS - 1

M1 - 48

ER -

Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

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Keywords

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