[1]汪亚楠,蔡耀雄.非局部Swift-Hohenberg方程的积分因子龙格库塔格式[J].华侨大学学报(自然科学版),2023,44(5):654-660.[doi:10.11830/ISSN.1000-5013.202210024]
 WANG Yanan,CAI Yaoxiong.Integrating Factor Runge-Kutta Format of Nonlocal Swift-Hohenberg Equation[J].Journal of Huaqiao University(Natural Science),2023,44(5):654-660.[doi:10.11830/ISSN.1000-5013.202210024]
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非局部Swift-Hohenberg方程的积分因子龙格库塔格式()
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《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第44卷
期数:
2023年第5期
页码:
654-660
栏目:
出版日期:
2023-09-20

文章信息/Info

Title:
Integrating Factor Runge-Kutta Format of Nonlocal Swift-Hohenberg Equation
文章编号:
1000-5013(2023)05-0654-07
作者:
汪亚楠 蔡耀雄
华侨大学 数学科学学院, 福建 泉州362021
Author(s):
WANG Yanan CAI Yaoxiong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
非局部Swift-Hohenberg方程 积分因子 龙格库塔 傅里叶谱方法
Keywords:
nonlocal Swift-Hohenberg equation integrating factor Runge-Kutta Fourier spectral method
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202210024
文献标志码:
A
摘要:
基于显式稳定性积分因子龙格库塔法和傅里叶谱方法,提出4种快速有效求解非局部Swift-Hohenberg方程的数值格式.通过4个数值算例验证格式的收敛性,并进行长时间动力行为的模拟.结果表明:文中算法具有良好的稳定性,且满足能量递减性质.
Abstract:
Based on the explicit stability integrating factor Runge-Kutta method and Fourier spectral method, four fast and effective numerical formats for solving nonlocal Swift-Hohenberg equations are proposed. Through four numerical examples, the convergence of the formats are verified, and the simulation of long-term dynamic behaviors are also carried out. The results show that the proposed algorithm has good stability and satisfies the property of decreasing energy.

参考文献/References:

[1] SWIFT J,HOHENBERG P C.Hydrodynamic fluctuations at the convective instability[J].Physical Review A,1977,15(1):319-328.DOI:10.1103/PhysRevA.15.319.
[2] HUTT A,ATAY F M.Analysis of nonlocal neural fields for both general and gamma-distributed connectivities[J].Physica D,2005,203(1/2):30-54.DOI:10.1016/j.physd.2005.03.002.
[3] HUTT A,LONGTIN A,SCHIMANSKY-GEIER L.Additive noise-induced turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation[J].Physica D,2008,237(6):755-773.DOI:10.1016/j.physd.2007.10.013.
[4] ROBERTS A J.The Swift-Hohenberg equation requires nonlocal modifications to model spatial pattern evolution of physical problems[EB/OL].(1994-12-09)[2022-10-05] .https://doi.org/10.48550/arXiv.patt-sol/9412002.
[5] MORGAN D,DAWES J H P.The Swift-Hohenberg equation with a nonlocal nonlinearity[J].Physica D,2014,270:60-80.DOI:10.1016/j.physd.2013.11.018.
[6] LIU Zhengguang,LI Xiaoli.Efficient modified techniques of invariant energy quadratization approach for gradient flows[J].Applied Mathematics Letters,2019,98:206-214.DOI:10.1016/j.aml.2019.06.006.
[7] SU Jian,FANG Weiwei,YU Qian,et al.Numerical simulation of Swift-Hohenberg equation by the fourth-order compact scheme[J].Computational and Applied Mathematics,2019,38(2):1-15.DOI:10.1007/s40314-019-0822-8.
[8] FIRTH W J,COLUMBO L,SCROGGIE A J.Proposed resolution of theory-experiment discrepancy in homoclinic snaking[J].Physical Review Letters,2007,99(10):104503.DOI:10.1103/PhysRevLett.99.104503.
[9] PURWINS H G,B?DEKER H U,AMIRANASHVIL S H.Dissipative solitons[J].Advances in Physics,2010,59(5):485-701.DOI:10.1080/00018732.2010.498228.
[10] DU Qiang,GUNZBURGER M,LEHOUCQ R B,et al.A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws[J].Mathematical Models and Methods in Applied Sciences,2013,23(3):493-540.DOI:10.1142/S0218202512500546.
[11] ZHANG Jun,YANG Xiaofeng.Numerical approximations for a new L2-gradient flowbased phase field crystal model with precise nonlocal mass conservation[J].Computer Physics Communications,2019,243:51-67.DOI:10.1016/j.cpc.2019.05.006.
[12] WENG Zhifeng,DENG Yangfang,ZHUANG Qingqu,et al.A fast and efficient numerical algorithm for Swift-Hohenberg equation with a nonlocal nonlinearity[J].Applied Mathematics Letters,2021,118:107170.DOI:10.1016/j.aml.2021.107170.
[13] JU Lili,LI Xiao,QIAO Zhonghua,et al.Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations[J].Journal of Computational Physics,2021,439:110405.DOI:10.1016/j.jcp.2021.110405.
[14] AHMED S,LIU Xinfeng.High order integration factor methods for systems with inhomogeneous boundary conditions[J].Journal of Computational and Applied Mathematics,2019,348:89-102.DOI:10.1016/j.cam.2018.08.036.
[15] ZHANG Hong,YAN Jingye,QIAN Xu,et al.Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations[J].Journal of Scientific Computing,2022,90(1):1-29.DOI:10.1007/s10915-021-01691-w.
[16] NAN Caixia,SONG Huailing.The high-order maximum-principle-preserving integrating factor Runge-Kutta methods for nonlocal Allen-Cahn equation[J].Journal of Computational Physics,2022,456:111028.DOI:10.1016/j.jcp.2022.111028.
[17] 刘飞.谱方法与高阶时间离散方法及应用[D].杭州:浙江大学,2012.
[18] SHU Chiwang,OSHER S.Efficient implementation of essentially non-oscillatory shock-capturing schemes[J].Journal of Computational Physics,1988,77(2):439-471.DOI:10.1016/0021-9991(88)90177-5.
[19] 李精伟.保证反应扩散方程物理性质的数值方法[D].乌鲁木齐:新疆大学,2020.
[20] ISHERWOOD L,GRANT Z J,GOTTLIEB S.Strong stability preserving integrating factor Runge-Kutta methods[J].SIAM Journal on Numerical Analysis,2018,56(6):3276-3307.DOI:10.1137/17M1143290.

备注/Memo

备注/Memo:
收稿日期: 2022-10-29
通信作者: 蔡耀雄(1979-),男,讲师,主要从事偏微分方程数值解及理论的研究.E-mail:cai_yx@126.com.
基金项目: 福建省自然科学基金资助项目(2020J01074)
更新日期/Last Update: 2023-09-20