Barycentric–Legendre Interpolation Method for Solving Two-Dimensional Fractional Cable Equation in Neuronal Dynamics

A. Rezazadeh; Z. Avazzadeh

doi:10.1007/s40819-022-01273-w

Barycentric–Legendre Interpolation Method for Solving Two-Dimensional Fractional Cable Equation in Neuronal Dynamics

A. Rezazadeh, Z. Avazzadeh^*

^*Corresponding author for this work

Department of Applied Mathematics

University of Qom

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

3 Citations (Scopus)

Abstract

This paper presents a spectral collocation method with the goal of estimating the solution of fractional cable equation in neuronal dynamics. The proposed method consists of expanding the unknown solution as the elements of the Barycentric basis and the shifted Legendre polynomials. The spatial derivative and time derivative are discretized using the Barycentric interpolation method and the Legendre polynomials, respectively. The differentiation matrix of the Barycentric method and the operational matrix of the Legendre polynomials are introduced. These matrices and the collocation points are applied to reduce the problem into a linear algebraic system. Eventually, some experimental examples are given to illustrate the efficiency and applicability of the method.

Original language	English
Article number	80
Journal	International Journal of Applied and Computational Mathematics
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s40819-022-01273-w
Publication status	Published - Apr 2022

Keywords

Barycenteric interpolation method
Caputo fractional derivative
Fractional cable equation
Operational matrix
Riemann–Liouville fractional derivative
Shifted Legendre polynomials

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title = "Barycentric–Legendre Interpolation Method for Solving Two-Dimensional Fractional Cable Equation in Neuronal Dynamics",

abstract = "This paper presents a spectral collocation method with the goal of estimating the solution of fractional cable equation in neuronal dynamics. The proposed method consists of expanding the unknown solution as the elements of the Barycentric basis and the shifted Legendre polynomials. The spatial derivative and time derivative are discretized using the Barycentric interpolation method and the Legendre polynomials, respectively. The differentiation matrix of the Barycentric method and the operational matrix of the Legendre polynomials are introduced. These matrices and the collocation points are applied to reduce the problem into a linear algebraic system. Eventually, some experimental examples are given to illustrate the efficiency and applicability of the method.",

keywords = "Barycenteric interpolation method, Caputo fractional derivative, Fractional cable equation, Operational matrix, Riemann–Liouville fractional derivative, Shifted Legendre polynomials",

author = "A. Rezazadeh and Z. Avazzadeh",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.",

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T1 - Barycentric–Legendre Interpolation Method for Solving Two-Dimensional Fractional Cable Equation in Neuronal Dynamics

AU - Rezazadeh, A.

AU - Avazzadeh, Z.

PY - 2022/4

Y1 - 2022/4

N2 - This paper presents a spectral collocation method with the goal of estimating the solution of fractional cable equation in neuronal dynamics. The proposed method consists of expanding the unknown solution as the elements of the Barycentric basis and the shifted Legendre polynomials. The spatial derivative and time derivative are discretized using the Barycentric interpolation method and the Legendre polynomials, respectively. The differentiation matrix of the Barycentric method and the operational matrix of the Legendre polynomials are introduced. These matrices and the collocation points are applied to reduce the problem into a linear algebraic system. Eventually, some experimental examples are given to illustrate the efficiency and applicability of the method.

AB - This paper presents a spectral collocation method with the goal of estimating the solution of fractional cable equation in neuronal dynamics. The proposed method consists of expanding the unknown solution as the elements of the Barycentric basis and the shifted Legendre polynomials. The spatial derivative and time derivative are discretized using the Barycentric interpolation method and the Legendre polynomials, respectively. The differentiation matrix of the Barycentric method and the operational matrix of the Legendre polynomials are introduced. These matrices and the collocation points are applied to reduce the problem into a linear algebraic system. Eventually, some experimental examples are given to illustrate the efficiency and applicability of the method.

KW - Barycenteric interpolation method

KW - Caputo fractional derivative

KW - Fractional cable equation

KW - Operational matrix

KW - Riemann–Liouville fractional derivative

KW - Shifted Legendre polynomials

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JO - International Journal of Applied and Computational Mathematics

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ER -

Barycentric–Legendre Interpolation Method for Solving Two-Dimensional Fractional Cable Equation in Neuronal Dynamics

Abstract

Keywords

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