A space-time spectral collocation method for the 2-dimensional nonlinear Riesz space fractional diffusion equations

Hui Li; Wei Jiang

doi:10.1002/mma.5124

A space-time spectral collocation method for the 2-dimensional nonlinear Riesz space fractional diffusion equations

Hui Li
, Wei Jiang^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

11 Scopus citations

Abstract

The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre-Gauss-Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first-order system of ordinary differential equation. Optimal priori error estimates in L² norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement.

Original language	English
Pages (from-to)	6130-6144
Number of pages	15
Journal	Mathematical Methods in the Applied Sciences
Volume	41
Issue number	16
DOIs	https://doi.org/10.1002/mma.5124
State	Published - 15 Nov 2018
Externally published	Yes

Keywords

Riesz fractional derivative
error estimates
nonlinear initial-value problems
space-time spectral method
spectral collocation method

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10.1002/mma.5124

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@article{2441149fe9d54fbd92d329589d6e7ab4,

title = "A space-time spectral collocation method for the 2-dimensional nonlinear Riesz space fractional diffusion equations",

abstract = "The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre-Gauss-Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement.",

keywords = "Riesz fractional derivative, error estimates, nonlinear initial-value problems, space-time spectral method, spectral collocation method",

author = "Hui Li and Wei Jiang",

note = "Publisher Copyright: Copyright {\textcopyright} 2018 John Wiley \& Sons, Ltd.",

year = "2018",

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TY - JOUR

T1 - A space-time spectral collocation method for the 2-dimensional nonlinear Riesz space fractional diffusion equations

AU - Li, Hui

AU - Jiang, Wei

PY - 2018/11/15

Y1 - 2018/11/15

N2 - The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre-Gauss-Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement.

AB - The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre-Gauss-Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first-order system of ordinary differential equation. Optimal priori error estimates in L2 norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement.

KW - Riesz fractional derivative

KW - error estimates

KW - nonlinear initial-value problems

KW - space-time spectral method

KW - spectral collocation method

UR - https://www.scopus.com/pages/publications/85055326012

U2 - 10.1002/mma.5124

DO - 10.1002/mma.5124

M3 - 文章

AN - SCOPUS:85055326012

SN - 0170-4214

VL - 41

SP - 6130

EP - 6144

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -

A space-time spectral collocation method for the 2-dimensional nonlinear Riesz space fractional diffusion equations

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Keywords

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