An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

Jingjun Zhao; Yu Li; Yang Xu

doi:10.1016/j.amc.2019.01.040

An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

Jingjun Zhao
, Yu Li
, Yang Xu^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Heilongjiang Bayi Agricultural University

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

11 Scopus citations

Abstract

In this paper, a new explicit fourth-order scheme for solving Riesz space fractional nonlinear wave equations is developed. The scheme is designed by using a novel Riesz space fractional difference operator for spatial discretization and a multidimensional extended Runge–Kutta–Nyström method for time integration. The conservation law of the semi-discrete energy, stability and convergence of the semi-discrete system are investigated. Numerical experiments show the efficiency and energy conservation of the present scheme.

Original language	English
Pages (from-to)	124-138
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	351
DOIs	https://doi.org/10.1016/j.amc.2019.01.040
State	Published - 15 Jun 2019

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Keywords

Energy conservation
Extended Runge–Kutta–Nyström method
Lubich difference operator
Riesz space fractional wave equation

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10.1016/j.amc.2019.01.040

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title = "An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations",

abstract = "In this paper, a new explicit fourth-order scheme for solving Riesz space fractional nonlinear wave equations is developed. The scheme is designed by using a novel Riesz space fractional difference operator for spatial discretization and a multidimensional extended Runge–Kutta–Nystr{\"o}m method for time integration. The conservation law of the semi-discrete energy, stability and convergence of the semi-discrete system are investigated. Numerical experiments show the efficiency and energy conservation of the present scheme.",

keywords = "Energy conservation, Extended Runge–Kutta–Nystr{\"o}m method, Lubich difference operator, Riesz space fractional wave equation",

author = "Jingjun Zhao and Yu Li and Yang Xu",

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

year = "2019",

month = jun,

day = "15",

doi = "10.1016/j.amc.2019.01.040",

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T1 - An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

AU - Zhao, Jingjun

AU - Li, Yu

AU - Xu, Yang

PY - 2019/6/15

Y1 - 2019/6/15

N2 - In this paper, a new explicit fourth-order scheme for solving Riesz space fractional nonlinear wave equations is developed. The scheme is designed by using a novel Riesz space fractional difference operator for spatial discretization and a multidimensional extended Runge–Kutta–Nyström method for time integration. The conservation law of the semi-discrete energy, stability and convergence of the semi-discrete system are investigated. Numerical experiments show the efficiency and energy conservation of the present scheme.

AB - In this paper, a new explicit fourth-order scheme for solving Riesz space fractional nonlinear wave equations is developed. The scheme is designed by using a novel Riesz space fractional difference operator for spatial discretization and a multidimensional extended Runge–Kutta–Nyström method for time integration. The conservation law of the semi-discrete energy, stability and convergence of the semi-discrete system are investigated. Numerical experiments show the efficiency and energy conservation of the present scheme.

KW - Energy conservation

KW - Extended Runge–Kutta–Nyström method

KW - Lubich difference operator

KW - Riesz space fractional wave equation

UR - https://www.scopus.com/pages/publications/85060696823

U2 - 10.1016/j.amc.2019.01.040

DO - 10.1016/j.amc.2019.01.040

M3 - 文章

AN - SCOPUS:85060696823

SN - 0096-3003

VL - 351

SP - 124

EP - 138

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

Abstract

UN SDGs

Keywords

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