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## Liao, Shijun

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 Author ID: liao.shijun Published as: Liao, Shijun; Liao, Shi-Jun; Liao, S. J.; Liao, S.-J.; Liao, ShiJun; Liao, Shi Jun; Liao, S. External Links: Wikidata · GND · IdRef
 Documents Indexed: 146 Publications since 1991, including 2 Books 2 Contributions as Editor
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#### Co-Authors

 60 single-authored 16 Xu, Hang 8 Lin, Zhiliang 5 Pop, Ioan 5 Zhao, Yinlong 4 Al-saedi, Ahmed Eid Salem 4 Liu, Zeng 4 Vajravelu, Kuppalapalle 4 Xie, Bin 4 Xu, Dali 4 Yang, Zhaochen 4 Zhu, Jimao 3 Cheng, Jun 3 Chwang, Allen Tseyung 3 Hayat, Tasawar 3 Li, Xiaoming 3 Mohapatra, Ram Narayan 3 Tan, Yue 3 Wang, Chun 3 Yu, Qiang 2 Abbasbandy, Saeid 2 Cang, Jie 2 Deng, Xi 2 Khan, Hina 2 Li, Rong-Kwei 2 Li, Xiaochen 2 Stiassnie, Michael Aharon 2 Wu, Yongyan 2 Xiao, Feng 2 Zhong, Xiaoxu 1 Borthwick, Alistair G. L. 1 Campo, Antonio 1 Chang, Chueh-Hsin 1 Chen, Jiankang 1 Cheung, Kwok Fai 1 Cui, Jifeng 1 Dias, Frédéric 1 Gaugler, Trent 1 Grebenev, Vladimir N. 1 He, Linghui 1 Jin, Peng 1 Kim, Daeyoung 1 Kousar, Nabeela 1 Li, Jing 1 Li, Jiyang 1 Li, Shuicai 1 Li, Yajie 1 Li, Zhibin 1 Liu, Yinping 1 Magyari, Eugen 1 Majdalani, Joseph 1 Mashayek, Farzad 1 Nakayama, Hiroki 1 Nohara, Ben T. 1 Oberlack, Martin 1 Rana, Jyotirmoy 1 Sheu, Tony Wen-Hann 1 Su, Jian 1 Sun, Bohua 1 Talay Akyildiz, F. 1 Wang, Ji 1 Wu, Guo Xiong 1 Wu, Jiezhi 1 Wu, Wan 1 Xu, Tianzhuang 1 Yang, Cheng 1 Yang, Xiaoyan 1 You, Xiangcheng 1 Yu, Ching-Hao 1 Zhu, Songping
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#### Serials

 27 Communications in Nonlinear Science and Numerical Simulation 12 International Journal for Numerical Methods in Fluids 9 Journal of Fluid Mechanics 9 Applied Mathematics and Computation 7 International Journal of Non-Linear Mechanics 5 International Journal of Heat and Mass Transfer 5 Chaos, Solitons and Fractals 5 Numerical Algorithms 5 European Journal of Mechanics. B. Fluids 3 Journal of Computational and Applied Mathematics 3 Applied Mathematics and Mechanics. (English Edition) 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Engineering Analysis with Boundary Elements 2 Acta Mechanica 2 Journal of Computational Physics 2 Wave Motion 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Studies in Applied Mathematics 2 Journal of Hydrodynamics. Ser. B 2 Journal of Non-Newtonian Fluid Mechanics 2 Nonlinear Dynamics 2 The ANZIAM Journal 2 Nonlinear Analysis. Real World Applications 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Computer Physics Communications 1 Journal of Applied Mechanics 1 Journal of Engineering Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 The Journal of the Indian Mathematical Society. New Series 1 Meccanica 1 Journal of Information & Optimization Sciences 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Computational Mechanics 1 Numerical Methods for Partial Differential Equations 1 Stochastic Hydrology and Hydraulics 1 Applied Mathematical Modelling 1 Communications in Statistics. Simulation and Computation 1 Celestial Mechanics and Dynamical Astronomy 1 Physics of Fluids 1 Journal of Statistics & Management Systems 1 Advances and Applications in Statistics 1 Journal of Systems Science and Complexity 1 AMM. Applied Mathematics and Mechanics. (English Edition)
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#### Fields

 76 Fluid mechanics (76-XX) 53 Numerical analysis (65-XX) 34 Partial differential equations (35-XX) 28 Ordinary differential equations (34-XX) 12 Classical thermodynamics, heat transfer (80-XX) 9 Mechanics of particles and systems (70-XX) 8 Mechanics of deformable solids (74-XX) 7 Dynamical systems and ergodic theory (37-XX) 3 Real functions (26-XX) 3 Computer science (68-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Statistics (62-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Sequences, series, summability (40-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

120 Publications have been cited 4,207 times in 1,474 Documents Cited by Year
On the homotopy analysis method for nonlinear problems. Zbl 1086.35005
Liao, Shijun
2004
Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001
Liao, Shijun
2004
Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126
Liao, Shijun
2009
An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. Zbl 1342.74180
Liao, Shi-Jun
1999
An approximate solution technique not depending on small parameters: A special example. Zbl 0837.76073
Liao, Shijun
1995
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Zbl 1063.76671
Liao, Shi-Jun
2003
A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. Zbl 0931.76017
Liao, Shijun
1999
A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142
Liao, Shijun
2005
An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088
Liao, Shijun
2010
Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534
Liao, Shijun
2005
A kind of approximation solution technique which does not depend upon small parameters. II: An application in fluid mechanics. Zbl 1031.76542
Liao, Shijun
1997
Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001
Liao, Shijun
2012
Analytic solutions of the temperature distribution in Blasius viscous flow problems. Zbl 1007.76014
Liao, Shijun; Campo, Antonio
2002
An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022
Liao, Shijun
2006
Homotopy analysis of nonlinear progressive waves in deep water. Zbl 1112.76316
Liao, Shi-Jun; Cheung, Kwok Fai
2003
Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008
Liao, Shijun; Pop, Ioan
2004
Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006
Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun
2009
A new analytic algorithm of Lane–Emden type equations. Zbl 1022.65078
Liao, Shijun
2003
An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354
Li, Shuicai; Liao, Shi-Jun
2005
Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009
Wu, Wan; Liao, Shijun
2005
Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. Zbl 1195.76069
Xu, Hang; Liao, Shi Jun
2005
A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046
Liao, Shi-Jun
2007
Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056
Liao, Shijun; Magyari, Eugen
2006
Series solutions of nano boundary layer flows by means of the homotopy analysis method. Zbl 1135.76016
Cheng, Jun; Liao, Shijun; Mohapatra, R. N.; Vajravelu, K.
2008
An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Zbl 1348.74225
Liao, Shi-Jun
2003
Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352
Liao, Shijun
2006
Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method. Zbl 1069.35060
Wu, Yongyan; Wang, Chun; Liao, Shi-Jun
2005
Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286
Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng
2009
Homotopy analysis method: A new analytic method for nonlinear problems. Zbl 1126.34311
Liao, Shijun
1998
An analytic approximation of the drag coefficient for the viscous flow past a sphere. Zbl 1116.76335
Liao, Shi-Jun
2002
An explicit analytic solution to the Thomas-Fermi equation. Zbl 1034.34005
Liao, Shijun
2003
Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032
Abbasbandy, S.; Tan, Y.; Liao, S. J.
2007
A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068
Liao, Shi-Jun
2009
An analytic approximate approach for free oscillations of self-excited systems. Zbl 1348.34071
Liao, Shi-Jun
2004
On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059
Yang, Cheng; Liao, Shijun
2006
Dual solutions of boundary layer flow over an upstream moving plate. Zbl 1131.35066
Xu, Hang; Liao, Shi-Jun
2008
Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Zbl 1190.76132
Xu, Hang; Lin, Zhi-Liang; Liao, Shi-Jun; Wu, Jie-Zhi; Majdalani, Joseph
2010
On the explicit analytic solution of Cheng-Chang equation. Zbl 1029.76050
Wang, C.; Zhu, J. M.; Liao, S. J.; Pop, I.
2003
Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body. Zbl 1189.76549
Liao, Shijun; Su, Jian; Chwang, Allen T.
2006
Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Zbl 1105.76061
Xu, Hang; Liao, Shijun; Pop, Ioan
2007
An explicit solution of the large deformation of a cantilever beam under point load at the free tip. Zbl 1128.74026
Wang, Ji; Chen, Jiankang; Liao, Shijun
2008
Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313
Tan, Yue; Xu, Hang; Liao, Shi-Jun
2007
A second-order approximate analytical solution of a simple pendulum by the process analysis method. Zbl 0769.70017
Liao, S. J.
1992
Numerically solving nonlinear problems by the homotopy analysis method. Zbl 0923.73076
Liao, S.-J.
1997
The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033
Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J.
2009
On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206
Liao, Shijun
2010
Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward stagnation point. Zbl 1195.76070
Xu, Hang; Liao, Shi Jun; Pop, Ioan
2006
On the steady-state fully resonant progressive waves in water of finite depth. Zbl 1275.76052
Xu, Dali; Lin, Zhiliang; Liao, Shijun; Stiassnie, Michael
2012
An explicit series approximation to the optimal exercise boundary of American put options. Zbl 1221.91053
Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun
2010
Homotopy analysis method: A new analytical technique for nonlinear problems. Zbl 0927.65069
Liao, Shijun
1997
On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046
Liao, Shi-Jun
2011
Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450
Liao, Shijun
2009
An analytical solution for a nonlinear time-delay model in biology. Zbl 1221.65204
Khan, Hina; Liao, Shi-Jun; Mohapatra, R. N.; Vajravelu, K.
2009
A short note on high-order streamfunction-vorticity formulations of 2D steady state Navier-Stokes equations. Zbl 0873.76052
Liao, Shijun; Zhu, Jimao
1996
Advances in the homotopy analysis method. Zbl 1283.35003
2014
Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet. Zbl 1186.76616
Xu, Hang; Liao, Shi-Jun
2009
An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate. Zbl 0922.34012
Liao, Shi-Jun
1998
A challenging nonlinear problem for numerical techniques. Zbl 1071.65112
Liao, ShiJun
2005
Series solutions of unsteady boundary-layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Zbl 1096.76004
Xu, H.; Liao, S. J.; Pop, I.
2006
Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Zbl 1311.70031
Li, Yajie; Nohara, Ben T.; Liao, Shijun
2010
A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falkner-Skan equation. Zbl 0990.76068
Liao, Shijun
2001
On the general boundary element method. Zbl 0940.65141
Liao, Shijun
1998
On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055
Liao, Shijun; Zhao, Yinlong
2016
Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. Zbl 1334.80004
Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun
2014
The scaled boundary FEM for nonlinear problems. Zbl 1221.65305
Lin, Zhiliang; Liao, Shijun
2011
On the steady-state nearly resonant waves. Zbl 1445.76023
Liao, Shijun; Xu, Dali; Stiassnie, Michael
2016
Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452
Xu, Hang; Liao, Shi-Jun
2006
The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099
Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun
2012
General boundary element method for nonlinear problems. Zbl 0863.76037
Liao, S. J.; Chwang, Allen T.
1996
A family of new solutions on the wall jet. Zbl 1154.76335
Xu, Hang; Liao, Shijun; Wu, Guo-Xiong
2008
On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007
Cheng, Jun; Cang, Jie; Liao, Shijun
2009
Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292
Liu, Y. P.; Liao, S. J.; Li, Z. B.
2013
A direct boundary element approach for unsteady nonlinear heat transfer problems. Zbl 0995.80008
Liao, Shijun
2002
High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. II: Some 2D examples. Zbl 0886.65111
Liao, Shijun
1997
A new modification of false position method based on homotopy analysis method. Zbl 1231.65084
Abbasbandy, Saeid; Liao, Shi-Jun
2008
The general boundary element method and its further generalizations. Zbl 0954.76060
Liao, Shijun
1999
High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. Zbl 0882.65108
Liao, Shijun
1996
A new method for homoclinic solutions of ordinary differential equations. Zbl 1197.65212
Akyildiz, F. Talay; Vajravelu, K.; Liao, S.-J.
2009
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
2013
On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087
Yang, Xiaoyan; Dias, Frederic; Liao, Shijun
2018
A short note on the general boundary element method for viscous flows with high Reynolds number. Zbl 1055.76037
Zhao, X. Y.; Liao, S. J.
2003
A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 07257658
Yang, Zhaochen; Liao, Shijun
2017
A novel homotopy-wavelet approach for solving stream function-vorticity formulation of Navier-Stokes equations. Zbl 1456.76107
Yu, Qiang; Xu, Hang; Liao, Shijun; Yang, Zhaochen
2019
Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations. Zbl 1460.74056
Yu, Qiang; Xu, Hang; Liao, Shijun
2018
Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach. Zbl 1433.65339
Yu, Qiang; Xu, Hang; Liao, Shijun
2018
Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM. Zbl 1221.76125
Lin, Zhiliang; Liao, Shijun
2011
The quite general BEM for strongly nonlinear problems. Zbl 0839.65132
Liao, S.-J.
1995
Some notes on the general boundary element method for highly nonlinear problems. Zbl 1147.76596
Wu, Y. Y.; Liao, S. J.; Zhao, X. Y.
2005
Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nano-fluid. Zbl 1410.76473
Farooq, U.; Zhao, Y. L.; Hayat, T.; Alsaedi, A.; Liao, S. J.
2015
A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 07261249
Yang, Zhaochen; Liao, Shijun
2017
Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026
Liu, Z.; Xu, D. L.; Liao, S. J.
2018
A simple approach of enlarging convergence regions of perturbation approximations. Zbl 0949.70003
Liao, Shijun
1999
General boundary element method for Poisson equation with spatially varying conductivity. Zbl 0940.65134
Liao, Shijun
1998
An explicit solution for the combined heat and mass transfer by natural convection from a vertical wall in a non-Darcy porous medium. Zbl 1046.76047
Wang, Chun; Liao, Shijun; Zhu, Jimao
2003
Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method. Zbl 1065.76152
Wu, Yongyan; Liao, Shijun
2005
Higher-order streamfunction-vorticity formulation of 2D steady-state Navier-Stokes equations. Zbl 0762.76063
Liao, S. J.
1992
A series solution of the unsteady von Kármán swirling viscous flows. Zbl 1122.35102
Xu, Hang; Liao, Shijun
2006
General boundary element method: An application of homotopy analysis method. Zbl 0918.65074
Liao, Shijun
1998
The general BEM and its applications in nonlinear heat transfer. Zbl 0867.65052
Liao, S.-J.; Chwang, A. T.
1996
Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet. Zbl 1206.35208
Kousar, Nabeela; Liao, Shijun
2011
A novel homotopy-wavelet approach for solving stream function-vorticity formulation of Navier-Stokes equations. Zbl 1456.76107
Yu, Qiang; Xu, Hang; Liao, Shijun; Yang, Zhaochen
2019
On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087
Yang, Xiaoyan; Dias, Frederic; Liao, Shijun
2018
Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations. Zbl 1460.74056
Yu, Qiang; Xu, Hang; Liao, Shijun
2018
Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach. Zbl 1433.65339
Yu, Qiang; Xu, Hang; Liao, Shijun
2018
Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026
Liu, Z.; Xu, D. L.; Liao, S. J.
2018
On the generalized wavelet-Galerkin method. Zbl 1377.65098
Yang, Zhaochen; Liao, Shijun
2018
A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 07257658
Yang, Zhaochen; Liao, Shijun
2017
A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 07261249
Yang, Zhaochen; Liao, Shijun
2017
Analytic solutions of Von Kármán plate under arbitrary uniform pressure – equations in differential form. Zbl 1367.74008
Zhong, X. X.; Liao, S. J.
2017
On the homotopy analysis method for backward/forward-backward stochastic differential equations. Zbl 1377.65009
Zhong, Xiaoxu; Liao, Shijun
2017
On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055
Liao, Shijun; Zhao, Yinlong
2016
On the steady-state nearly resonant waves. Zbl 1445.76023
Liao, Shijun; Xu, Dali; Stiassnie, Michael
2016
Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nano-fluid. Zbl 1410.76473
Farooq, U.; Zhao, Y. L.; Hayat, T.; Alsaedi, A.; Liao, S. J.
2015
Equilibrium states of class-I Bragg resonant wave system. Zbl 1408.76093
Xu, Dali; Lin, Zhiliang; Liao, Shijun
2015
Development of a numerical phase optimized upwinding combined compact difference scheme for solving the Camassa-Holm equation with different initial solitary waves. Zbl 1331.65132
Yu, C. H.; Sheu, Tony W. H.; Chang, C. H.; Liao, S. J.
2015
Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces. Zbl 1329.76256
Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, S. J.
2015
On the inherent self-excited macroscopic randomness of chaotic three-body systems. Zbl 1325.70022
Liao, Shijun; Li, Xiaoming
2015
A HAM-based analytic approach for physical models with an infinite number of singularities. Zbl 1314.65136
Xu, Dali; Cui, Jifeng; Liao, Shijun; Alsaedi, A.
2015
Advances in the homotopy analysis method. Zbl 1283.35003
2014
Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. Zbl 1334.80004
Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun
2014
Can we obtain a reliable convergent chaotic solution in any given finite interval of time? Zbl 1301.34059
Liao, Shijun
2014
Physical limit of prediction for chaotic motion of three-body problem. Zbl 1473.70019
Liao, Shijun
2014
Phase velocity effects of the wave interaction with exponentially sheared current. Zbl 1456.76022
Liu, Zeng; Lin, Zhiliang; Liao, Shijun
2014
HAM-based Mathematica package BVPh 2.0 for nonlinear boundary value problems. Zbl 1301.65082
Zhao, Yinlong; Liao, Shijun
2014
Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292
Liu, Y. P.; Liao, S. J.; Li, Z. B.
2013
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
2013
Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001
Liao, Shijun
2012
On the steady-state fully resonant progressive waves in water of finite depth. Zbl 1275.76052
Xu, Dali; Lin, Zhiliang; Liao, Shijun; Stiassnie, Michael
2012
The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099
Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun
2012
A Maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations. Zbl 1255.93054
Liu, Yinping; Liao, Shijun; Li, Zhibin
2012
On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046
Liao, Shi-Jun
2011
The scaled boundary FEM for nonlinear problems. Zbl 1221.65305
Lin, Zhiliang; Liao, Shijun
2011
Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM. Zbl 1221.76125
Lin, Zhiliang; Liao, Shijun
2011
Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet. Zbl 1206.35208
Kousar, Nabeela; Liao, Shijun
2011
An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088
Liao, Shijun
2010
Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Zbl 1190.76132
Xu, Hang; Lin, Zhi-Liang; Liao, Shi-Jun; Wu, Jie-Zhi; Majdalani, Joseph
2010
On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206
Liao, Shijun
2010
An explicit series approximation to the optimal exercise boundary of American put options. Zbl 1221.91053
Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun
2010
Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Zbl 1311.70031
Li, Yajie; Nohara, Ben T.; Liao, Shijun
2010
Explicit series solution of a closure model for the von Kármán-Howarth equation. Zbl 1235.34065
Liu, Zeng; Oberlack, Martin; Grebenev, Vladimir N.; Liao, Shi-Jun
2010
Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126
Liao, Shijun
2009
Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006
Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun
2009
Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286
Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng
2009
A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068
Liao, Shi-Jun
2009
The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033
Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J.
2009
Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450
Liao, Shijun
2009
An analytical solution for a nonlinear time-delay model in biology. Zbl 1221.65204
Khan, Hina; Liao, Shi-Jun; Mohapatra, R. N.; Vajravelu, K.
2009
Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet. Zbl 1186.76616
Xu, Hang; Liao, Shi-Jun
2009
On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007
Cheng, Jun; Cang, Jie; Liao, Shijun
2009
A new method for homoclinic solutions of ordinary differential equations. Zbl 1197.65212
Akyildiz, F. Talay; Vajravelu, K.; Liao, S.-J.
2009
Series solution of large deformation of a beam with arbitrary variable cross section under an axial load. Zbl 1196.34027
Liao, Shijun
2009
Series solutions of nano boundary layer flows by means of the homotopy analysis method. Zbl 1135.76016
Cheng, Jun; Liao, Shijun; Mohapatra, R. N.; Vajravelu, K.
2008
Dual solutions of boundary layer flow over an upstream moving plate. Zbl 1131.35066
Xu, Hang; Liao, Shi-Jun
2008
An explicit solution of the large deformation of a cantilever beam under point load at the free tip. Zbl 1128.74026
Wang, Ji; Chen, Jiankang; Liao, Shijun
2008
A family of new solutions on the wall jet. Zbl 1154.76335
Xu, Hang; Liao, Shijun; Wu, Guo-Xiong
2008
A new modification of false position method based on homotopy analysis method. Zbl 1231.65084
Abbasbandy, Saeid; Liao, Shi-Jun
2008
A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046
Liao, Shi-Jun
2007
Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032
Abbasbandy, S.; Tan, Y.; Liao, S. J.
2007
Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Zbl 1105.76061
Xu, Hang; Liao, Shijun; Pop, Ioan
2007
Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313
Tan, Yue; Xu, Hang; Liao, Shi-Jun
2007
An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022
Liao, Shijun
2006
Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056
Liao, Shijun; Magyari, Eugen
2006
Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352
Liao, Shijun
2006
On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059
Yang, Cheng; Liao, Shijun
2006
Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body. Zbl 1189.76549
Liao, Shijun; Su, Jian; Chwang, Allen T.
2006
Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward stagnation point. Zbl 1195.76070
Xu, Hang; Liao, Shi Jun; Pop, Ioan
2006
Series solutions of unsteady boundary-layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Zbl 1096.76004
Xu, H.; Liao, S. J.; Pop, I.
2006
Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452
Xu, Hang; Liao, Shi-Jun
2006
A series solution of the unsteady von Kármán swirling viscous flows. Zbl 1122.35102
Xu, Hang; Liao, Shijun
2006
A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142
Liao, Shijun
2005
Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534
Liao, Shijun
2005
An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354
Li, Shuicai; Liao, Shi-Jun
2005
Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009
Wu, Wan; Liao, Shijun
2005
Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. Zbl 1195.76069
Xu, Hang; Liao, Shi Jun
2005
Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method. Zbl 1069.35060
Wu, Yongyan; Wang, Chun; Liao, Shi-Jun
2005
A challenging nonlinear problem for numerical techniques. Zbl 1071.65112
Liao, ShiJun
2005
Some notes on the general boundary element method for highly nonlinear problems. Zbl 1147.76596
Wu, Y. Y.; Liao, S. J.; Zhao, X. Y.
2005
Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method. Zbl 1065.76152
Wu, Yongyan; Liao, Shijun
2005
On the homotopy analysis method for nonlinear problems. Zbl 1086.35005
Liao, Shijun
2004
Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001
Liao, Shijun
2004
Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008
Liao, Shijun; Pop, Ioan
2004
An analytic approximate approach for free oscillations of self-excited systems. Zbl 1348.34071
Liao, Shi-Jun
2004
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Zbl 1063.76671
Liao, Shi-Jun
2003
Homotopy analysis of nonlinear progressive waves in deep water. Zbl 1112.76316
Liao, Shi-Jun; Cheung, Kwok Fai
2003
A new analytic algorithm of Lane–Emden type equations. Zbl 1022.65078
Liao, Shijun
2003
An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Zbl 1348.74225
Liao, Shi-Jun
2003
An explicit analytic solution to the Thomas-Fermi equation. Zbl 1034.34005
Liao, Shijun
2003
On the explicit analytic solution of Cheng-Chang equation. Zbl 1029.76050
Wang, C.; Zhu, J. M.; Liao, S. J.; Pop, I.
2003
A short note on the general boundary element method for viscous flows with high Reynolds number. Zbl 1055.76037
Zhao, X. Y.; Liao, S. J.
2003
An explicit solution for the combined heat and mass transfer by natural convection from a vertical wall in a non-Darcy porous medium. Zbl 1046.76047
Wang, Chun; Liao, Shijun; Zhu, Jimao
2003
On a generalized Taylor theorem: a rational proof of the validity of the homotopy analysis method. Zbl 1044.41019
Liao, Shijun
2003
An explicit analytic solution for non-Darcy natural convection over horizontal plate with surface mass flux and thermal dispersion effects. Zbl 1064.76103
Wang, C.; Liao, S. J.; Zhu, J. M.
2003
Analytic solutions of the temperature distribution in Blasius viscous flow problems. Zbl 1007.76014
Liao, Shijun; Campo, Antonio
2002
An analytic approximation of the drag coefficient for the viscous flow past a sphere. Zbl 1116.76335
Liao, Shi-Jun
2002
A direct boundary element approach for unsteady nonlinear heat transfer problems. Zbl 0995.80008
Liao, Shijun
2002
A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falkner-Skan equation. Zbl 0990.76068
Liao, Shijun
2001
An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. Zbl 1342.74180
Liao, Shi-Jun
1999
A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. Zbl 0931.76017
Liao, Shijun
1999
The general boundary element method and its further generalizations. Zbl 0954.76060
Liao, Shijun
1999
A simple approach of enlarging convergence regions of perturbation approximations. Zbl 0949.70003
Liao, Shijun
1999
...and 20 more Documents
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all top 5

#### Cited in 188 Serials

 132 Communications in Nonlinear Science and Numerical Simulation 114 Applied Mathematics and Computation 64 Mathematical Problems in Engineering 45 Computers & Mathematics with Applications 44 Chaos, Solitons and Fractals 43 Numerical Algorithms 39 International Journal for Numerical Methods in Fluids 38 Applied Mathematical Modelling 35 Abstract and Applied Analysis 32 Applied Mathematics and Mechanics. (English Edition) 30 Journal of Applied Mathematics 29 AMM. Applied Mathematics and Mechanics. (English Edition) 28 International Journal of Numerical Methods for Heat & Fluid Flow 27 Meccanica 26 Journal of Computational and Applied Mathematics 25 Numerical Methods for Partial Differential Equations 25 Advances in Difference Equations 24 Mathematical Methods in the Applied Sciences 22 International Journal of Applied and Computational Mathematics 21 Engineering Analysis with Boundary Elements 21 Nonlinear Dynamics 20 Acta Mechanica 20 Mathematical and Computer Modelling 19 Advances in Mathematical Physics 18 Computational and Applied Mathematics 17 Mathematics and Computers in Simulation 16 International Journal of Heat and Mass Transfer 16 Nonlinear Analysis. Real World Applications 15 Journal of Applied Mechanics and Technical Physics 15 European Journal of Mechanics. B. Fluids 12 Computers and Fluids 11 Journal of Fluid Mechanics 11 International Journal of Computer Mathematics 11 Boundary Value Problems 10 Journal of Mathematical Chemistry 9 Acta Mechanica Sinica 9 International Journal of Biomathematics 9 International Journal of Differential Equations 9 Advances in Applied Mathematics and Mechanics 9 Mathematical Sciences 8 Physics Letters. A 8 Acta Applicandae Mathematicae 8 Discrete Dynamics in Nature and Society 8 Journal of Applied Mathematics and Computing 7 Afrika Matematika 6 International Journal of Engineering Science 6 Applied Mathematics Letters 6 Journal of the Egyptian Mathematical Society 6 Journal of Mathematics 5 International Journal of Modern Physics B 5 Computer Physics Communications 5 Journal of Computational Physics 5 Wave Motion 5 Mechanics Research Communications 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Complexity 5 Journal of Vibration and Control 5 International Journal of Computational Methods 5 Asian-European Journal of Mathematics 5 International Journal of Structural Stability and Dynamics 4 Indian Journal of Pure & Applied Mathematics 4 Journal of the Franklin Institute 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Physics 4 Applied Numerical Mathematics 4 Computational Mathematics and Mathematical Physics 4 Chaos 4 The ANZIAM Journal 4 Differential Equations & Nonlinear Mechanics 4 Arabian Journal for Science and Engineering 4 S$$\vec{\text{e}}$$MA Journal 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Archive of Applied Mechanics 3 Differential Equations and Dynamical Systems 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Mathematical Modelling and Analysis 3 Journal of Systems Science and Complexity 3 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 3 The Journal of Prime Research in Mathematics 3 International Journal for Numerical Methods in Biomedical Engineering 3 Symmetry 3 Mathematics 3 Journal of Computational Methods in Physics 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Engineering 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Studies in Applied Mathematics 2 Chinese Annals of Mathematics. Series B 2 Computational Mechanics 2 Journal of Elasticity 2 Physics of Fluids 2 Filomat 2 International Journal of Computational Fluid Dynamics 2 Fractional Calculus & Applied Analysis 2 European Journal of Mechanics. A. Solids 2 Quantitative Finance 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Inverse Problems in Science and Engineering ...and 88 more Serials
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#### Cited in 42 Fields

 594 Fluid mechanics (76-XX) 556 Numerical analysis (65-XX) 350 Partial differential equations (35-XX) 304 Ordinary differential equations (34-XX) 203 Classical thermodynamics, heat transfer (80-XX) 125 Mechanics of deformable solids (74-XX) 88 Biology and other natural sciences (92-XX) 55 Integral equations (45-XX) 53 Real functions (26-XX) 31 Dynamical systems and ergodic theory (37-XX) 26 Mechanics of particles and systems (70-XX) 21 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Operator theory (47-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 16 Statistical mechanics, structure of matter (82-XX) 14 Systems theory; control (93-XX) 13 Probability theory and stochastic processes (60-XX) 12 Computer science (68-XX) 11 Approximations and expansions (41-XX) 10 Integral transforms, operational calculus (44-XX) 10 Optics, electromagnetic theory (78-XX) 9 Special functions (33-XX) 9 Quantum theory (81-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Astronomy and astrophysics (85-XX) 5 Geophysics (86-XX) 5 Operations research, mathematical programming (90-XX) 4 Statistics (62-XX) 4 Information and communication theory, circuits (94-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Difference and functional equations (39-XX) 3 Algebraic topology (55-XX) 2 Measure and integration (28-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX)

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