Space-time spectral method for the Cattaneo equation with time fractional derivative

Hui Li; Wei Jiang; Wenya Li

doi:10.1016/j.amc.2018.12.050

Space-time spectral method for the Cattaneo equation with time fractional derivative

Hui Li
, Wei Jiang^*
, Wenya Li

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

16 Scopus citations

Abstract

This paper introduces a high-order accurate numerical method for solving the Cattaneo equation with time fractional derivative. It is based on the Galerkin–Legendre spectral method in space and the Chebyshev collocation method in time. Arbitrarily high-order accurate can be made in both space and time. Optimal priori error bound of the semi-discrete method and the stability and convergence of the full-discrete method are strictly given. Extensive experimental results confirm the theoretical claims of this method in both space and time.

Original language	English
Pages (from-to)	325-336
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	349
DOIs	https://doi.org/10.1016/j.amc.2018.12.050
State	Published - 15 May 2019
Externally published	Yes

Keywords

Cattaneo equation
Error estimates
Galerkin–Legendre spectral method
Space-time spectral method
Spectral collocation scheme

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10.1016/j.amc.2018.12.050

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title = "Space-time spectral method for the Cattaneo equation with time fractional derivative",

abstract = "This paper introduces a high-order accurate numerical method for solving the Cattaneo equation with time fractional derivative. It is based on the Galerkin–Legendre spectral method in space and the Chebyshev collocation method in time. Arbitrarily high-order accurate can be made in both space and time. Optimal priori error bound of the semi-discrete method and the stability and convergence of the full-discrete method are strictly given. Extensive experimental results confirm the theoretical claims of this method in both space and time.",

keywords = "Cattaneo equation, Error estimates, Galerkin–Legendre spectral method, Space-time spectral method, Spectral collocation scheme",

author = "Hui Li and Wei Jiang and Wenya Li",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = may,

day = "15",

doi = "10.1016/j.amc.2018.12.050",

language = "英语",

volume = "349",

pages = "325--336",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

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TY - JOUR

T1 - Space-time spectral method for the Cattaneo equation with time fractional derivative

AU - Li, Hui

AU - Jiang, Wei

AU - Li, Wenya

PY - 2019/5/15

Y1 - 2019/5/15

N2 - This paper introduces a high-order accurate numerical method for solving the Cattaneo equation with time fractional derivative. It is based on the Galerkin–Legendre spectral method in space and the Chebyshev collocation method in time. Arbitrarily high-order accurate can be made in both space and time. Optimal priori error bound of the semi-discrete method and the stability and convergence of the full-discrete method are strictly given. Extensive experimental results confirm the theoretical claims of this method in both space and time.

AB - This paper introduces a high-order accurate numerical method for solving the Cattaneo equation with time fractional derivative. It is based on the Galerkin–Legendre spectral method in space and the Chebyshev collocation method in time. Arbitrarily high-order accurate can be made in both space and time. Optimal priori error bound of the semi-discrete method and the stability and convergence of the full-discrete method are strictly given. Extensive experimental results confirm the theoretical claims of this method in both space and time.

KW - Cattaneo equation

KW - Error estimates

KW - Galerkin–Legendre spectral method

KW - Space-time spectral method

KW - Spectral collocation scheme

UR - https://www.scopus.com/pages/publications/85059816082

U2 - 10.1016/j.amc.2018.12.050

DO - 10.1016/j.amc.2018.12.050

M3 - 文章

AN - SCOPUS:85059816082

SN - 0096-3003

VL - 349

SP - 325

EP - 336

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Space-time spectral method for the Cattaneo equation with time fractional derivative

Abstract

Keywords

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