A local refinement purely meshless scheme for time fractional nonlinear Schrödinger equation in irregular geometry region

A local refinement hybrid scheme (LRCSPH-FDM) is proposed to solve the two-dimensional (2D) time fractional nonlinear Schrödinger equation (TF-NLSE) in regularly or irregularly shaped domains, and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross–P...

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Published inChinese physics B Vol. 30; no. 2; p. 20202
Main Authors Jiang, Tao, Jiang, Rong-Rong, Huang, Jin-Jing, Ding, Jiu, Ren, Jin-Lian
Format Journal Article
LanguageEnglish
Published 01.02.2021
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Abstract A local refinement hybrid scheme (LRCSPH-FDM) is proposed to solve the two-dimensional (2D) time fractional nonlinear Schrödinger equation (TF-NLSE) in regularly or irregularly shaped domains, and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross–Pitaevskii equation (TF-GPE) with the rotating Bose–Einstein condensate. It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge. The proposed LRCSPH-FDM (which is based on a local refinement corrected SPH method combined with FDM) is derived by using the finite difference scheme (FDM) to discretize the Caputo TF term, followed by using a corrected smoothed particle hydrodynamics (CSPH) scheme continuously without using the kernel derivative to approximate the spatial derivatives. Meanwhile, the local refinement technique is adopted to reduce the numerical error. In numerical simulations, the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method. The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D (where 1D stands for one-dimensional) analytical TF-NLSEs in a rectangular region (with regular or irregular particle distribution) or in a region with irregular geometry. The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain, and the results from the posed method are compared with those from the FDM. All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.
AbstractList A local refinement hybrid scheme (LRCSPH-FDM) is proposed to solve the two-dimensional (2D) time fractional nonlinear Schrödinger equation (TF-NLSE) in regularly or irregularly shaped domains, and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross–Pitaevskii equation (TF-GPE) with the rotating Bose–Einstein condensate. It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge. The proposed LRCSPH-FDM (which is based on a local refinement corrected SPH method combined with FDM) is derived by using the finite difference scheme (FDM) to discretize the Caputo TF term, followed by using a corrected smoothed particle hydrodynamics (CSPH) scheme continuously without using the kernel derivative to approximate the spatial derivatives. Meanwhile, the local refinement technique is adopted to reduce the numerical error. In numerical simulations, the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method. The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D (where 1D stands for one-dimensional) analytical TF-NLSEs in a rectangular region (with regular or irregular particle distribution) or in a region with irregular geometry. The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain, and the results from the posed method are compared with those from the FDM. All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.
Author Huang, Jin-Jing
Ding, Jiu
Jiang, Tao
Jiang, Rong-Rong
Ren, Jin-Lian
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Cites_doi 10.1186/s13662-018-1743-3
10.1016/j.cpc.2014.10.004
10.1155/2013/290216
10.5402/2012/197068
10.1016/j.jcp.2007.02.001
10.1002/(ISSN)1097-0207
10.1142/5340
10.1103/PhysRevE.66.056108
10.1088/1674-1056/24/10/100201
10.1063/1.1769611
10.1115/1.1431547
10.1007/s11071-011-0014-6
10.1016/j.jcp.2018.12.043
10.1016/j.cnsns.2018.11.013
10.1016/j.jcp.2004.11.001
10.3970/cmes.2014.100.399
10.1016/j.amc.2018.04.019
10.1016/j.jcp.2017.11.003
10.1016/0010-4655(94)00174-Z
10.1137/080714130
10.1007/s11831-010-9040-7
10.1016/j.cpc.2016.04.014
10.1016/j.cpc.2018.05.007
10.1137/1018042
10.1016/j.apm.2012.01.012
10.1088/1674-1056/25/4/040204
10.1137/16M1103622
10.1016/j.jcp.2013.03.007
10.1088/1674-1056/ab3af3
10.1016/j.aml.2018.05.007
10.1016/j.jmaa.2008.03.061
10.1016/j.apm.2018.03.043
10.4208/cicp.OA-2017-0195
10.1016/j.cpc.2018.02.013
10.1016/S0375-9601(00)00201-2
10.26713%2Fcma.v7i1.327
10.4310/CMS.2005.v3.n1.a5
10.1016/j.apm.2005.05.003
10.1016/j.amc.2004.10.066
10.1016/j.jcp.2017.03.061
10.1016/j.cma.2016.10.028
10.1016/j.jcp.2006.01.020
10.1016/j.cnsns.2017.06.018
10.1016/j.jcp.2014.09.023
10.1002/nme.4960
10.12691/ajma-1-1-3
10.1016/j.camwa.2016.07.036
10.1016/S0021-9991(03)00102-5
10.1002/nme.v88.13
10.1016/S0034-4877(16)30002-7
10.1016/j.jcp.2016.10.022
10.1016/S0045-7825(99)00422-3
10.1063/1.5006955
10.1002/num.22126
10.1016/j.chaos.2011.03.005
10.1007/s00466-013-0943-7
10.1016/j.apm.2014.08.011
10.1016/j.jcp.2015.03.063
10.1016/j.jcp.2013.11.017
10.1103/PhysRevLett.120.130402
10.1016/j.cam.2008.07.008
10.1016/j.apm.2013.12.001
10.1016/j.enganabound.2012.12.002
10.1006/jcph.1997.5776
10.1016/j.physa.2016.10.071
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References Basic (cpb_30_2_020202bib45) 2018; 354
Shivanian (cpb_30_2_020202bib44) 2015; 105
Gao (cpb_30_2_020202bib66) 2014; 259
Bao (cpb_30_2_020202bib12) 2005; 3
Narahari Achar (cpb_30_2_020202bib5) 2013; 2013
Chen (cpb_30_2_020202bib21) 2019; 71
Liu (cpb_30_2_020202bib56) 2010; 17
Chen (cpb_30_2_020202bib39) 2017; 468
Xu (cpb_30_2_020202bib30) 2005; 205
Sulem (cpb_30_2_020202bib13) 1990
Iomin (cpb_30_2_020202bib20) 2011; 44
Sun (cpb_30_2_020202bib58) 2017; 315
Ozkan (cpb_30_2_020202bib26) 2015; 24
Deng (cpb_30_2_020202bib9) 2009; 47
Quinlan (cpb_30_2_020202bib49) 2016; 66
Zhang (cpb_30_2_020202bib8) 2018; 335
Azzouzi (cpb_30_2_020202bib34) 2015; 39
Liu (cpb_30_2_020202bib64) 2005; 29
Wang (cpb_30_2_020202bib10) 2005; 170
Liu (cpb_30_2_020202bib47) 2003
Aboelenen (cpb_30_2_020202bib31) 2018; 54
Liu (cpb_30_2_020202bib55) 2019; 384
Zhuang (cpb_30_2_020202bib43) 2011; 88
Chen (cpb_30_2_020202bib25) 2018; 84
Zhou (cpb_30_2_020202bib67) 2018; 120
Li (cpb_30_2_020202bib23) 2018; 318
Abdel-Salam (cpb_30_2_020202bib29) 2016; 77
Zhang (cpb_30_2_020202bib37) 2019; 25
Morris (cpb_30_2_020202bib61) 1997; 136
Li (cpb_30_2_020202bib52) 2002; 55
Mohebbi (cpb_30_2_020202bib46) 2013; 37
Wang (cpb_30_2_020202bib68) 2013; 243
Jiang (cpb_30_2_020202bib62) 2014; 53
Gong (cpb_30_2_020202bib41) 2017; 328
Laskin (cpb_30_2_020202bib17) 2000; 268
Chen (cpb_30_2_020202bib33) 2018; 28
Shivanian (cpb_30_2_020202bib32) 2017; 33
Mohebbi (cpb_30_2_020202bib28) 2009; 225
Dong (cpb_30_2_020202bib22) 2008; 344
Naber (cpb_30_2_020202bib19) 2004; 45
Wilson (cpb_30_2_020202bib16) 2019; 235
Crespo (cpb_30_2_020202bib57) 2015; 187
Garrappa (cpb_30_2_020202bib42) 2015; 293
Tayebi (cpb_30_2_020202bib54) 2017; 340
Laskin (cpb_30_2_020202bib18) 2002; 66
Podlubny (cpb_30_2_020202bib2) 1999
Hicdurmaz (cpb_30_2_020202bib24) 2016; 72
Dehghan (cpb_30_2_020202bib53) 2014; 100
Bhrawy (cpb_30_2_020202bib36) 2015; 294
Ray (cpb_30_2_020202bib6) 2016; 25
Herzallah (cpb_30_2_020202bib35) 2012; 36
Chen (cpb_30_2_020202bib48) 2000; 190
Mao (cpb_30_2_020202bib3) 2018; 56
Alzaidy (cpb_30_2_020202bib7) 2013; 1
Lin (cpb_30_2_020202bib40) 2007; 225
Hu (cpb_30_2_020202bib4) 2019; 28
Edeki (cpb_30_2_020202bib27) 2016; 7
Bao (cpb_30_2_020202bib11) 2003; 187
Monaghan (cpb_30_2_020202bib60) 1995; 87
Khan (cpb_30_2_020202bib38) 2012; 2012
Jiang (cpb_30_2_020202bib50) 2018; 231
Lavoie (cpb_30_2_020202bib1) 1976; 18
Bao (cpb_30_2_020202bib14) 2006; 217
Yang (cpb_30_2_020202bib63) 2014; 38
Ren (cpb_30_2_020202bib59) 2016; 205
Ei-Danaf (cpb_30_2_020202bib15) 2012; 67
Jiang (cpb_30_2_020202bib51) 2019; 68
Zhang (cpb_30_2_020202bib65) 2018; 60
References_xml – volume: 318
  start-page: 1687
  year: 2018
  ident: cpb_30_2_020202bib23
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-018-1743-3
  contributor:
    fullname: Li
– volume: 187
  start-page: 204
  year: 2015
  ident: cpb_30_2_020202bib57
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2014.10.004
  contributor:
    fullname: Crespo
– volume: 2013
  year: 2013
  ident: cpb_30_2_020202bib5
  publication-title: Adv. Math. Phys.
  doi: 10.1155/2013/290216
  contributor:
    fullname: Narahari Achar
– volume: 2012
  year: 2012
  ident: cpb_30_2_020202bib38
  publication-title: ISRN Math. Phys.
  doi: 10.5402/2012/197068
  contributor:
    fullname: Khan
– volume: 225
  start-page: 1533
  year: 2007
  ident: cpb_30_2_020202bib40
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2007.02.001
  contributor:
    fullname: Lin
– volume: 66
  start-page: 2064
  year: 2016
  ident: cpb_30_2_020202bib49
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/(ISSN)1097-0207
  contributor:
    fullname: Quinlan
– year: 2003
  ident: cpb_30_2_020202bib47
  doi: 10.1142/5340
  contributor:
    fullname: Liu
– volume: 66
  year: 2002
  ident: cpb_30_2_020202bib18
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.66.056108
  contributor:
    fullname: Laskin
– volume: 24
  year: 2015
  ident: cpb_30_2_020202bib26
  publication-title: Chin. Phys. B
  doi: 10.1088/1674-1056/24/10/100201
  contributor:
    fullname: Ozkan
– volume: 45
  start-page: 3339
  year: 2004
  ident: cpb_30_2_020202bib19
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1769611
  contributor:
    fullname: Naber
– volume: 55
  start-page: 1
  year: 2002
  ident: cpb_30_2_020202bib52
  publication-title: Appl. Mech. Rev.
  doi: 10.1115/1.1431547
  contributor:
    fullname: Li
– volume: 67
  start-page: 619
  year: 2012
  ident: cpb_30_2_020202bib15
  publication-title: Nonlinear Dyn.
  doi: 10.1007/s11071-011-0014-6
  contributor:
    fullname: Ei-Danaf
– volume: 384
  start-page: 222
  year: 2019
  ident: cpb_30_2_020202bib55
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2018.12.043
  contributor:
    fullname: Liu
– volume: 71
  start-page: 73
  year: 2019
  ident: cpb_30_2_020202bib21
  publication-title: Commun. Nonlinear Sci. Numer. Simulat.
  doi: 10.1016/j.cnsns.2018.11.013
  contributor:
    fullname: Chen
– volume: 205
  start-page: 72
  year: 2005
  ident: cpb_30_2_020202bib30
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2004.11.001
  contributor:
    fullname: Xu
– volume: 68
  year: 2019
  ident: cpb_30_2_020202bib51
  publication-title: Acta Phys. Sin.
  doi: 10.3970/cmes.2014.100.399
  contributor:
    fullname: Jiang
– volume: 335
  start-page: 305
  year: 2018
  ident: cpb_30_2_020202bib8
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2018.04.019
  contributor:
    fullname: Zhang
– volume: 354
  start-page: 269
  year: 2018
  ident: cpb_30_2_020202bib45
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2017.11.003
  contributor:
    fullname: Basic
– volume: 87
  start-page: 225
  year: 1995
  ident: cpb_30_2_020202bib60
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/0010-4655(94)00174-Z
  contributor:
    fullname: Monaghan
– volume: 47
  start-page: 204
  year: 2009
  ident: cpb_30_2_020202bib9
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/080714130
  contributor:
    fullname: Deng
– volume: 17
  start-page: 25
  year: 2010
  ident: cpb_30_2_020202bib56
  publication-title: Arch. Comput. Methods Eng.
  doi: 10.1007/s11831-010-9040-7
  contributor:
    fullname: Liu
– volume: 205
  start-page: 87
  year: 2016
  ident: cpb_30_2_020202bib59
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2016.04.014
  contributor:
    fullname: Ren
– volume: 231
  start-page: 19
  year: 2018
  ident: cpb_30_2_020202bib50
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2018.05.007
  contributor:
    fullname: Jiang
– year: 1999
  ident: cpb_30_2_020202bib2
  contributor:
    fullname: Podlubny
– volume: 18
  start-page: 240
  year: 1976
  ident: cpb_30_2_020202bib1
  publication-title: SIAM Rev.
  doi: 10.1137/1018042
  contributor:
    fullname: Lavoie
– volume: 36
  start-page: 5678
  year: 2012
  ident: cpb_30_2_020202bib35
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2012.01.012
  contributor:
    fullname: Herzallah
– volume: 25
  year: 2016
  ident: cpb_30_2_020202bib6
  publication-title: Chin. Phys. B
  doi: 10.1088/1674-1056/25/4/040204
  contributor:
    fullname: Ray
– volume: 56
  start-page: 24
  year: 2018
  ident: cpb_30_2_020202bib3
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/16M1103622
  contributor:
    fullname: Mao
– volume: 243
  start-page: 382
  year: 2013
  ident: cpb_30_2_020202bib68
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2013.03.007
  contributor:
    fullname: Wang
– volume: 28
  year: 2019
  ident: cpb_30_2_020202bib4
  publication-title: Chin. Phys. B
  doi: 10.1088/1674-1056/ab3af3
  contributor:
    fullname: Hu
– volume: 84
  start-page: 160
  year: 2018
  ident: cpb_30_2_020202bib25
  publication-title: Appl. Math. Lett.
  doi: 10.1016/j.aml.2018.05.007
  contributor:
    fullname: Chen
– volume: 344
  start-page: 1005
  year: 2008
  ident: cpb_30_2_020202bib22
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2008.03.061
  contributor:
    fullname: Dong
– volume: 60
  start-page: 606
  year: 2018
  ident: cpb_30_2_020202bib65
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2018.03.043
  contributor:
    fullname: Zhang
– volume: 25
  start-page: 218
  year: 2019
  ident: cpb_30_2_020202bib37
  publication-title: Commun. Comput. Phys.
  doi: 10.4208/cicp.OA-2017-0195
  contributor:
    fullname: Zhang
– volume: 235
  start-page: 279
  year: 2019
  ident: cpb_30_2_020202bib16
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2018.02.013
  contributor:
    fullname: Wilson
– volume: 268
  start-page: 298
  year: 2000
  ident: cpb_30_2_020202bib17
  publication-title: Phys. Lett. A
  doi: 10.1016/S0375-9601(00)00201-2
  contributor:
    fullname: Laskin
– volume: 7
  start-page: 1
  year: 2016
  ident: cpb_30_2_020202bib27
  publication-title: Commun. Math. Appl.
  doi: 10.26713%2Fcma.v7i1.327
  contributor:
    fullname: Edeki
– volume: 3
  start-page: 57
  year: 2005
  ident: cpb_30_2_020202bib12
  publication-title: Commun. Math. Sci
  doi: 10.4310/CMS.2005.v3.n1.a5
  contributor:
    fullname: Bao
– volume: 29
  start-page: 1252
  year: 2005
  ident: cpb_30_2_020202bib64
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2005.05.003
  contributor:
    fullname: Liu
– volume: 170
  start-page: 17
  year: 2005
  ident: cpb_30_2_020202bib10
  publication-title: Appl. Math. Comput
  doi: 10.1016/j.amc.2004.10.066
  contributor:
    fullname: Wang
– volume: 340
  start-page: 655
  year: 2017
  ident: cpb_30_2_020202bib54
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2017.03.061
  contributor:
    fullname: Tayebi
– volume: 315
  start-page: 25
  year: 2017
  ident: cpb_30_2_020202bib58
  publication-title: Comput. Meth. Appl. Mech. Eng.
  doi: 10.1016/j.cma.2016.10.028
  contributor:
    fullname: Sun
– volume: 217
  start-page: 612
  year: 2006
  ident: cpb_30_2_020202bib14
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2006.01.020
  contributor:
    fullname: Bao
– volume: 54
  start-page: 428
  year: 2018
  ident: cpb_30_2_020202bib31
  publication-title: Commun. Nonlinear Sci. Numer. Simulat.
  doi: 10.1016/j.cnsns.2017.06.018
  contributor:
    fullname: Aboelenen
– volume: 293
  start-page: 115
  year: 2015
  ident: cpb_30_2_020202bib42
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2014.09.023
  contributor:
    fullname: Garrappa
– volume: 105
  start-page: 83
  year: 2015
  ident: cpb_30_2_020202bib44
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.4960
  contributor:
    fullname: Shivanian
– volume: 1
  start-page: 14
  year: 2013
  ident: cpb_30_2_020202bib7
  publication-title: Amer. J. Math. Anal.
  doi: 10.12691/ajma-1-1-3
  contributor:
    fullname: Alzaidy
– volume: 72
  start-page: 1703
  year: 2016
  ident: cpb_30_2_020202bib24
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2016.07.036
  contributor:
    fullname: Hicdurmaz
– volume: 187
  start-page: 318
  year: 2003
  ident: cpb_30_2_020202bib11
  publication-title: J. Comput. Phys.
  doi: 10.1016/S0021-9991(03)00102-5
  contributor:
    fullname: Bao
– volume: 88
  start-page: 1346
  year: 2011
  ident: cpb_30_2_020202bib43
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.v88.13
  contributor:
    fullname: Zhuang
– volume: 77
  start-page: 19
  year: 2016
  ident: cpb_30_2_020202bib29
  publication-title: Rep. Math. Phys.
  doi: 10.1016/S0034-4877(16)30002-7
  contributor:
    fullname: Abdel-Salam
– volume: 328
  start-page: 354
  year: 2017
  ident: cpb_30_2_020202bib41
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2016.10.022
  contributor:
    fullname: Gong
– volume: 190
  start-page: 225
  year: 2000
  ident: cpb_30_2_020202bib48
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/S0045-7825(99)00422-3
  contributor:
    fullname: Chen
– volume: 28
  year: 2018
  ident: cpb_30_2_020202bib33
  publication-title: Chaos
  doi: 10.1063/1.5006955
  contributor:
    fullname: Chen
– volume: 33
  start-page: 1043
  year: 2017
  ident: cpb_30_2_020202bib32
  publication-title: Numer. Methods Partial Differ. Equ.
  doi: 10.1002/num.22126
  contributor:
    fullname: Shivanian
– volume: 44
  start-page: 348
  year: 2011
  ident: cpb_30_2_020202bib20
  publication-title: Chaos, Solitons & Fractals
  doi: 10.1016/j.chaos.2011.03.005
  contributor:
    fullname: Iomin
– volume: 53
  start-page: 977
  year: 2014
  ident: cpb_30_2_020202bib62
  publication-title: Comput. Mech.
  doi: 10.1007/s00466-013-0943-7
  contributor:
    fullname: Jiang
– volume: 39
  start-page: 1300
  year: 2015
  ident: cpb_30_2_020202bib34
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2014.08.011
  contributor:
    fullname: Azzouzi
– volume: 294
  start-page: 462
  year: 2015
  ident: cpb_30_2_020202bib36
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2015.03.063
  contributor:
    fullname: Bhrawy
– volume: 259
  start-page: 33
  year: 2014
  ident: cpb_30_2_020202bib66
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2013.11.017
  contributor:
    fullname: Gao
– year: 1990
  ident: cpb_30_2_020202bib13
  contributor:
    fullname: Sulem
– volume: 120
  year: 2018
  ident: cpb_30_2_020202bib67
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.120.130402
  contributor:
    fullname: Zhou
– volume: 225
  start-page: 124
  year: 2009
  ident: cpb_30_2_020202bib28
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/j.cam.2008.07.008
  contributor:
    fullname: Mohebbi
– volume: 38
  start-page: 3822
  year: 2014
  ident: cpb_30_2_020202bib63
  publication-title: Appl. Math. Model.
  doi: 10.1016/j.apm.2013.12.001
  contributor:
    fullname: Yang
– volume: 37
  start-page: 475
  year: 2013
  ident: cpb_30_2_020202bib46
  publication-title: Eng. Anal. Bound. Elem.
  doi: 10.1016/j.enganabound.2012.12.002
  contributor:
    fullname: Mohebbi
– volume: 100
  start-page: 399
  year: 2014
  ident: cpb_30_2_020202bib53
  publication-title: Cmes-Comp. Model. Eng.
  doi: 10.3970/cmes.2014.100.399
  contributor:
    fullname: Dehghan
– volume: 136
  start-page: 214
  year: 1997
  ident: cpb_30_2_020202bib61
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.1997.5776
  contributor:
    fullname: Morris
– volume: 468
  start-page: 532
  year: 2017
  ident: cpb_30_2_020202bib39
  publication-title: Physica A
  doi: 10.1016/j.physa.2016.10.071
  contributor:
    fullname: Chen
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Snippet A local refinement hybrid scheme (LRCSPH-FDM) is proposed to solve the two-dimensional (2D) time fractional nonlinear Schrödinger equation (TF-NLSE) in...
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Title A local refinement purely meshless scheme for time fractional nonlinear Schrödinger equation in irregular geometry region
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