A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations

Wei Jiang; Hui Li

doi:10.1016/j.camwa.2018.02.013

A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations

Wei Jiang^*
, Hui Li

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

19 Scopus citations

Abstract

In this article, we introduce a space–time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre–Gauss–Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in L² norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.

Original language	English
Pages (from-to)	3508-3520
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	75
Issue number	10
DOIs	https://doi.org/10.1016/j.camwa.2018.02.013
State	Published - 15 May 2018
Externally published	Yes

Keywords

Error estimates
Fractional derivative of variable order
Fractional percolation equation
Space–time spectral collocation method

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10.1016/j.camwa.2018.02.013

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title = "A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations",

abstract = "In this article, we introduce a space–time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre–Gauss–Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.",

keywords = "Error estimates, Fractional derivative of variable order, Fractional percolation equation, Space–time spectral collocation method",

author = "Wei Jiang and Hui Li",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

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T1 - A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations

AU - Jiang, Wei

AU - Li, Hui

PY - 2018/5/15

Y1 - 2018/5/15

N2 - In this article, we introduce a space–time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre–Gauss–Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.

AB - In this article, we introduce a space–time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre–Gauss–Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.

KW - Error estimates

KW - Fractional derivative of variable order

KW - Fractional percolation equation

KW - Space–time spectral collocation method

UR - https://www.scopus.com/pages/publications/85042933336

U2 - 10.1016/j.camwa.2018.02.013

DO - 10.1016/j.camwa.2018.02.013

M3 - 文章

AN - SCOPUS:85042933336

SN - 0898-1221

VL - 75

SP - 3508

EP - 3520

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 10

ER -

A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations

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Keywords

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