×
Author ID: liao.shijun Recent zbMATH articles by "Liao, Shijun"
Published as: Liao, Shijun; Liao, Shi-Jun; Liao, S. J.; Liao, ShiJun; Liao, Shi Jun; Liao, S.-J.; Liao, S.
External Links: Wikidata · GND · IdRef
all top 5

Serials

27 Communications in Nonlinear Science and Numerical Simulation
12 International Journal for Numerical Methods in Fluids
12 Journal of Fluid Mechanics
9 Applied Mathematics and Computation
7 International Journal of Non-Linear Mechanics
6 Chaos, Solitons and Fractals
6 European Journal of Mechanics. B. Fluids
5 International Journal of Heat and Mass Transfer
5 Numerical Algorithms
4 Journal of Computational Physics
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
3 Advances in Applied Mathematics and Mechanics
2 Acta Mechanica
2 Wave Motion
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Studies in Applied Mathematics
2 Computational Mechanics
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 Physica D
1 Journal of Symbolic Computation
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)

Publications by Year

Citations contained in zbMATH Open

141 Publications have been cited 4,701 times in 1,888 Documents Cited by Year
On the homotopy analysis method for nonlinear problems. Zbl 1086.35005
Liao, Shijun
480
2004
Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001
Liao, Shijun
368
2004
Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126
Liao, Shijun
246
2009
An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. Zbl 1342.74180
Liao, Shi-Jun
197
1999
An approximate solution technique not depending on small parameters: A special example. Zbl 0837.76073
Liao, Shijun
196
1995
An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088
Liao, Shijun
172
2010
Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001
Liao, Shijun
169
2012
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Zbl 1063.76671
Liao, Shi-Jun
168
2003
A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142
Liao, Shijun
162
2005
A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. Zbl 0931.76017
Liao, Shijun
162
1999
Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534
Liao, Shijun
143
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
131
1997
Analytic solutions of the temperature distribution in Blasius viscous flow problems. Zbl 1007.76014
Liao, Shijun; Campo, Antonio
108
2002
An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022
Liao, Shijun
102
2006
Homotopy analysis of nonlinear progressive waves in deep water. Zbl 1112.76316
Liao, Shi-Jun; Cheung, Kwok Fai
101
2003
Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008
Liao, Shijun; Pop, Ioan
64
2004
A new analytic algorithm of Lane–Emden type equations. Zbl 1022.65078
Liao, Shijun
62
2003
Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006
Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun
62
2009
An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354
Li, Shuicai; Liao, Shi-Jun
58
2005
Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009
Wu, Wan; Liao, Shijun
52
2005
Homotopy analysis method: A new analytic method for nonlinear problems. Zbl 1126.34311
Liao, Shijun
50
1998
Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. Zbl 1195.76069
Xu, Hang; Liao, Shi Jun
49
2005
A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046
Liao, Shi-Jun
48
2007
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.
45
2008
Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056
Liao, Shijun; Magyari, Eugen
45
2006
An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Zbl 1348.74225
Liao, Shi-Jun
40
2003
Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352
Liao, Shijun
40
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
39
2005
Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032
Abbasbandy, S.; Tan, Y.; Liao, S. J.
38
2007
Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286
Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng
38
2009
A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068
Liao, Shi-Jun
38
2009
An explicit analytic solution to the Thomas-Fermi equation. Zbl 1034.34005
Liao, Shijun
37
2003
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
36
2010
An analytic approximation of the drag coefficient for the viscous flow past a sphere. Zbl 1116.76335
Liao, Shi-Jun
35
2002
An analytic approximate approach for free oscillations of self-excited systems. Zbl 1348.34071
Liao, Shi-Jun
35
2004
On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059
Yang, Cheng; Liao, Shijun
33
2006
Dual solutions of boundary layer flow over an upstream moving plate. Zbl 1131.35066
Xu, Hang; Liao, Shi-Jun
33
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
31
2008
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
29
2007
On the explicit analytic solution of Cheng-Chang equation. Zbl 1029.76050
Wang, C.; Zhu, J. M.; Liao, S. J.; Pop, I.
28
2003
Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313
Tan, Yue; Xu, Hang; Liao, Shi-Jun
27
2007
Homotopy analysis method: A new analytical technique for nonlinear problems. Zbl 0927.65069
Liao, Shijun
27
1997
The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033
Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J.
27
2009
A second-order approximate analytical solution of a simple pendulum by the process analysis method. Zbl 0769.70017
Liao, S. J.
27
1992
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.
27
2006
Numerically solving nonlinear problems by the homotopy analysis method. Zbl 0923.73076
Liao, S.-J.
25
1997
On the steady-state fully resonant progressive waves in water of finite depth. Zbl 1275.76052
Xu, Dali; Lin, Zhiliang; Liao, Shijun; Stiassnie, Michael
25
2012
A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 1510.65311
Yang, Zhaochen; Liao, Shijun
23
2017
An explicit series approximation to the optimal exercise boundary of American put options. Zbl 1221.91053
Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun
22
2010
On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206
Liao, Shijun
20
2010
On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046
Liao, Shi-Jun
20
2011
Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450
Liao, Shijun
20
2009
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
19
2006
An analytical solution for a nonlinear time-delay model in biology. Zbl 1221.65204
Khan, Hina; Liao, Shi-Jun; Mohapatra, R. N.; Vajravelu, K.
18
2009
A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 1510.65181
Yang, Zhaochen; Liao, Shijun
17
2017
Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Zbl 1311.70031
Li, Yajie; Nohara, Ben T.; Liao, Shijun
14
2010
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
13
2009
A short note on high-order streamfunction-vorticity formulations of 2D steady state Navier-Stokes equations. Zbl 0873.76052
Liao, Shijun; Zhu, Jimao
13
1996
On the steady-state nearly resonant waves. Zbl 1445.76023
Liao, Shijun; Xu, Dali; Stiassnie, Michael
13
2016
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
13
2019
On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055
Liao, Shijun; Zhao, Yinlong
13
2016
Advances in the homotopy analysis method. Zbl 1283.35003
13
2014
General boundary element method for nonlinear heat transfer problems governed by hyperbolic heat conduction equation. Zbl 0890.65121
Liao, S.
12
1997
An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate. Zbl 0922.34012
Liao, Shi-Jun
12
1998
Physical limit of prediction for chaotic motion of three-body problem. Zbl 1473.70019
Liao, Shijun
12
2014
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.
11
2006
A challenging nonlinear problem for numerical techniques. Zbl 1071.65112
Liao, ShiJun
11
2005
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
11
2014
Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452
Xu, Hang; Liao, Shi-Jun
10
2006
A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falkner-Skan equation. Zbl 0990.76068
Liao, Shijun
10
2001
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
10
2018
On the general boundary element method. Zbl 0940.65141
Liao, Shijun
9
1998
The scaled boundary FEM for nonlinear problems. Zbl 1221.65305
Lin, Zhiliang; Liao, Shijun
9
2011
On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007
Cheng, Jun; Cang, Jie; Liao, Shijun
9
2009
General boundary element method for nonlinear problems. Zbl 0863.76037
Liao, S. J.; Chwang, Allen T.
9
1996
High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow. Zbl 1452.76137
Xie, Bin; Deng, Xi; Liao, ShiJun; Xiao, Feng
9
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
9
2018
A family of new solutions on the wall jet. Zbl 1154.76335
Xu, Hang; Liao, Shijun; Wu, Guo-Xiong
8
2008
The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099
Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun
8
2012
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
8
2013
On the risks of using double precision in numerical simulations of spatio-temporal chaos. Zbl 07506180
Hu, Tianli; Liao, Shijun
8
2020
On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087
Yang, Xiaoyan; Dias, Frederic; Liao, Shijun
8
2018
A direct boundary element approach for unsteady nonlinear heat transfer problems. Zbl 0995.80008
Liao, Shijun
7
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
7
1997
A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids. Zbl 1453.76116
Xie, Bin; Jin, Peng; Nakayama, Hiroki; Liao, ShiJun; Xiao, Feng
7
2020
Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292
Liu, Y. P.; Liao, S. J.; Li, Z. B.
7
2013
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.
7
2015
Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026
Liu, Z.; Xu, D. L.; Liao, S. J.
7
2018
The general boundary element method and its further generalizations. Zbl 0954.76060
Liao, Shijun
6
1999
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.
6
2003
Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method. Zbl 1065.76152
Wu, Yongyan; Liao, Shijun
6
2005
High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. Zbl 0882.65108
Liao, Shijun
6
1996
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.
6
2015
Analytic solutions of Von Kármán plate under arbitrary uniform pressure – equations in differential form. Zbl 1367.74008
Zhong, X. X.; Liao, S. J.
6
2017
A new modification of false position method based on homotopy analysis method. Zbl 1231.65084
Abbasbandy, Saeid; Liao, Shi-Jun
6
2008
A new method for homoclinic solutions of ordinary differential equations. Zbl 1197.65212
Akyildiz, F. Talay; Vajravelu, K.; Liao, S.-J.
6
2009
Influence of numerical noises on computer-generated simulation of spatio-temporal chaos. Zbl 1489.65163
Qin, Shijie; Liao, Shijun
6
2020
The quite general BEM for strongly nonlinear problems. Zbl 0839.65132
Liao, S.-J.
5
1995
Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM. Zbl 1221.76125
Lin, Zhiliang; Liao, Shijun
5
2011
Some notes on the general boundary element method for highly nonlinear problems. Zbl 1147.76596
Wu, Y. Y.; Liao, S. J.; Zhao, X. Y.
5
2005
A kind of Lagrangian chaotic property of the Arnold-Beltrami-Childress flow. Zbl 1520.76036
Qin, Shijie; Liao, Shijun
2
2023
Avoiding small denominator problems by means of the homotopy analysis method. Zbl 1524.65301
Liao, Shijun
1
2023
Ultra-chaos: an insurmountable objective obstacle of reproducibility and replication. Zbl 1499.35445
Liao, Shijun; Qin, Shijie
2
2022
Wave breaking and jet formation on axisymmetric surface gravity waves. Zbl 07465425
McAllister, M. L.; Draycott, S.; Davey, T.; Yang, Y.; Adcock, T. A. A.; Liao, S.; van den Bremer, T. S.
2
2022
Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method. Zbl 07508446
Xie, Bin; Deng, Xi; Liao, ShiJun; Xiao, Feng
2
2021
Triple collision orbits in the free-fall three-body system without binary collisions. Zbl 1490.70046
Li, Xiaoming; Li, Xiaochen; He, Linghui; Liao, Shijun
1
2021
Finite-amplitude steady-state resonant waves in a circular basin. Zbl 1497.76017
Yang, Xiaoyan; Dias, Frederic; Liu, Zeng; Liao, Shijun
1
2021
On the risks of using double precision in numerical simulations of spatio-temporal chaos. Zbl 07506180
Hu, Tianli; Liao, Shijun
8
2020
A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids. Zbl 1453.76116
Xie, Bin; Jin, Peng; Nakayama, Hiroki; Liao, ShiJun; Xiao, Feng
7
2020
Influence of numerical noises on computer-generated simulation of spatio-temporal chaos. Zbl 1489.65163
Qin, Shijie; Liao, Shijun
6
2020
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
13
2019
High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow. Zbl 1452.76137
Xie, Bin; Deng, Xi; Liao, ShiJun; Xiao, Feng
9
2019
High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow. Zbl 1442.65208
Xie, Bin; Deng, Xi; Liao, Shijun
4
2019
Analytic solutions of the rise dynamics of liquid in a vertical cylindrical capillary. Zbl 1476.76031
Zhong, Xiaoxu; Sun, Bohua; Liao, Shijun
1
2019
Stability and hysteresis of Faraday waves in Hele-Shaw cells. Zbl 1419.76225
Li, Jing; Li, Xiaochen; Liao, Shijun
1
2019
A general analytical approach to study solute dispersion in non-Newtonian fluid flow. Zbl 1475.76088
Rana, Jyotirmoy; Liao, Shijun
1
2019
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
10
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
9
2018
On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087
Yang, Xiaoyan; Dias, Frederic; Liao, Shijun
8
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.
7
2018
On the generalized wavelet-Galerkin method. Zbl 1377.65098
Yang, Zhaochen; Liao, Shijun
5
2018
Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems. Zbl 1404.37094
Li, Xiaoming; Liao, Shijun
2
2018
A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 1510.65311
Yang, Zhaochen; Liao, Shijun
23
2017
A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 1510.65181
Yang, Zhaochen; Liao, Shijun
17
2017
Analytic solutions of Von Kármán plate under arbitrary uniform pressure – equations in differential form. Zbl 1367.74008
Zhong, X. X.; Liao, S. J.
6
2017
On the homotopy analysis method for backward/forward-backward stochastic differential equations. Zbl 1377.65009
Zhong, Xiaoxu; Liao, Shijun
3
2017
On the steady-state nearly resonant waves. Zbl 1445.76023
Liao, Shijun; Xu, Dali; Stiassnie, Michael
13
2016
On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055
Liao, Shijun; Zhao, Yinlong
13
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.
7
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.
6
2015
On the inherent self-excited macroscopic randomness of chaotic three-body systems. Zbl 1325.70022
Liao, Shijun; Li, Xiaoming
5
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.
2
2015
Equilibrium states of class-I Bragg resonant wave system. Zbl 1408.76093
Xu, Dali; Lin, Zhiliang; Liao, Shijun
2
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.
1
2015
Advances in the homotopy analysis method. Zbl 1283.35003
13
2014
Physical limit of prediction for chaotic motion of three-body problem. Zbl 1473.70019
Liao, Shijun
12
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
11
2014
HAM-based Mathematica package BVPh 2.0 for nonlinear boundary value problems. Zbl 1301.65082
Zhao, Yinlong; Liao, Shijun
4
2014
Can we obtain a reliable convergent chaotic solution in any given finite interval of time? Zbl 1301.34059
Liao, Shijun
3
2014
Preface. Zbl 1302.00066
1
2014
Phase velocity effects of the wave interaction with exponentially sheared current. Zbl 1456.76022
Liu, Zeng; Lin, Zhiliang; Liao, Shijun
1
2014
Do peaked solitary water waves indeed exist? Zbl 1457.35057
Liao, Shijun
1
2014
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
8
2013
Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292
Liu, Y. P.; Liao, S. J.; Li, Z. B.
7
2013
Two new standing solitary waves in shallow water. Zbl 1454.76031
Liao, Shijun
1
2013
Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001
Liao, Shijun
169
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
25
2012
The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099
Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun
8
2012
A Maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations. Zbl 1255.93054
Liu, Yinping; Liao, Shijun; Li, Zhibin
1
2012
On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046
Liao, Shi-Jun
20
2011
The scaled boundary FEM for nonlinear problems. Zbl 1221.65305
Lin, Zhiliang; Liao, Shijun
9
2011
Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM. Zbl 1221.76125
Lin, Zhiliang; Liao, Shijun
5
2011
Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet. Zbl 1206.35208
Kousar, Nabeela; Liao, Shijun
2
2011
An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088
Liao, Shijun
172
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
36
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
22
2010
On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206
Liao, Shijun
20
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
14
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
1
2010
Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126
Liao, Shijun
246
2009
Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006
Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun
62
2009
Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286
Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng
38
2009
A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068
Liao, Shi-Jun
38
2009
The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033
Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J.
27
2009
Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450
Liao, Shijun
20
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.
18
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
13
2009
On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007
Cheng, Jun; Cang, Jie; Liao, Shijun
9
2009
A new method for homoclinic solutions of ordinary differential equations. Zbl 1197.65212
Akyildiz, F. Talay; Vajravelu, K.; Liao, S.-J.
6
2009
Series solution of large deformation of a beam with arbitrary variable cross section under an axial load. Zbl 1196.34027
Liao, Shijun
1
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.
45
2008
Dual solutions of boundary layer flow over an upstream moving plate. Zbl 1131.35066
Xu, Hang; Liao, Shi-Jun
33
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
31
2008
A family of new solutions on the wall jet. Zbl 1154.76335
Xu, Hang; Liao, Shijun; Wu, Guo-Xiong
8
2008
A new modification of false position method based on homotopy analysis method. Zbl 1231.65084
Abbasbandy, Saeid; Liao, Shi-Jun
6
2008
A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046
Liao, Shi-Jun
48
2007
Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032
Abbasbandy, S.; Tan, Y.; Liao, S. J.
38
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
29
2007
Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313
Tan, Yue; Xu, Hang; Liao, Shi-Jun
27
2007
An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022
Liao, Shijun
102
2006
Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056
Liao, Shijun; Magyari, Eugen
45
2006
Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352
Liao, Shijun
40
2006
On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059
Yang, Cheng; Liao, Shijun
33
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.
27
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
19
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.
11
2006
Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452
Xu, Hang; Liao, Shi-Jun
10
2006
A series solution of the unsteady von Kármán swirling viscous flows. Zbl 1122.35102
Xu, Hang; Liao, Shijun
3
2006
A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142
Liao, Shijun
162
2005
Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534
Liao, Shijun
143
2005
An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354
Li, Shuicai; Liao, Shi-Jun
58
2005
Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009
Wu, Wan; Liao, Shijun
52
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
49
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
39
2005
A challenging nonlinear problem for numerical techniques. Zbl 1071.65112
Liao, ShiJun
11
2005
Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method. Zbl 1065.76152
Wu, Yongyan; Liao, Shijun
6
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.
5
2005
On the homotopy analysis method for nonlinear problems. Zbl 1086.35005
Liao, Shijun
480
2004
Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001
Liao, Shijun
368
2004
Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008
Liao, Shijun; Pop, Ioan
64
2004
...and 41 more Documents
all top 5

Cited by 2,351 Authors

186 Hayat, Tasawar
90 Liao, Shijun
65 Al-saedi, Ahmed Eid Salem
47 Abbasbandy, Saeid
43 Sajid, Muhammad
43 Xu, Hang
39 Vajravelu, Kuppalapalle
36 Ganji, Davood Domiri
34 Pop, Ioan
32 Băleanu, Dumitru I.
32 van Gorder, Robert Ashton
29 Asghar, Saleem
28 Hashim, Ishak
27 Rashidi, Mohammad Mehdi
25 Kumar, Devendra
25 Motsa, Sandile Sydney
24 Abbas, Zaheer
21 Noorani, Mohd Salmi Mohd
21 Shehzad, Sabir Ali
21 Singh, Jagdev
20 Alomari, Abedel-Karrem
18 Muhammad, Taseer
18 Zheng, Liancun
17 Ayub, Muhammad
17 Odibat, Zaid M.
17 Veeresha, Pundikala
16 Ellahi, Rahmat
16 Nazar, Roslinda Mohd
16 Sibanda, Precious
15 Dinarvand, Saeed
15 Fang, Tiegang
15 Mustafa, Meraj
15 Prakasha, Doddabhadrappla Gowda
14 Nadeem, Sohail
14 Shateyi, Stanford
14 Turkyilmazoglu, Mustafa
13 Dehghan Takht Fooladi, Mehdi
13 Javed, Tariq
13 Kiliçman, Adem
13 Zhang, Xinxin
12 Bataineh, Ahmad Sami
12 Kumar, Sunil
12 Momani, Shaher M.
12 Saad, Khaled Mohammed
11 Islam, Saeed
11 Yıldırım, Ahmet
10 Awais, Muhammad
10 de la Sen, Manuel
10 Jafari, Hossein
10 Khan, Masood
10 Parand, Kourosh
10 Roul, Pradip
9 Akinyemi, Lanre
9 Alonso Quesada, Santiago
9 Baskonus, Haci Mehmet
9 Gómez-Aguilar, José Francisco
9 Ibeas, Asier
9 Ishak, Anuar
9 Obaidat, Saleem A.
9 Ramos, Juan I.
9 Shivanian, Elyas
9 Xie, Bin
9 Yu, Qiang
8 He, Jihuan
8 Lin, Zhiliang
8 Liu, Zeng
8 Si, Xinhui
7 Ariel, P. Donald
7 Awawdeh, Fadi
7 Bararnia, H.
7 Dewasurendra, Mangalagama
7 Imtiaz, Maria
7 Khan, Yasir
7 Kumar, Amit
7 Molabahrami, Ahmad
7 Naz, Rahila
7 Shidfar, Abdollah
7 Singh, Randhir
7 Xiao, Feng
7 Zhang, Ji
6 Abdulaziz, O.
6 Ali, Nasir
6 Deng, Xi
6 Duarte, Jorge A.
6 Effati, Sohrab
6 Fariborzi Araghi, Mohammad Ali
6 Januário, Cristina
6 Khan, Ilyas
6 Kimiaeifar, A.
6 Kumaran, Vishwanathan
6 Li, Lin
6 Liang, Songxin
6 Martins, Nuno
6 Noor, Muhammad Aslam
6 Qasim, Muhammad
6 Qian, Youhua
6 Rabbani, Mohsen
6 Srivastava, Hari Mohan
6 Syam, Muhammed I.
6 Vázquez-Leal, Héctor
...and 2,251 more Authors
all top 5

Cited in 223 Serials

151 Communications in Nonlinear Science and Numerical Simulation
134 Applied Mathematics and Computation
69 Mathematical Problems in Engineering
58 Chaos, Solitons and Fractals
55 Computers & Mathematics with Applications
51 Applied Mathematical Modelling
46 Numerical Algorithms
40 International Journal for Numerical Methods in Fluids
37 Advances in Difference Equations
37 International Journal of Applied and Computational Mathematics
36 Abstract and Applied Analysis
33 Applied Mathematics and Mechanics. (English Edition)
33 Numerical Methods for Partial Differential Equations
32 AMM. Applied Mathematics and Mechanics. (English Edition)
31 Mathematical Methods in the Applied Sciences
31 International Journal of Numerical Methods for Heat & Fluid Flow
30 Journal of Applied Mathematics
29 Journal of Computational and Applied Mathematics
27 Meccanica
26 Computational and Applied Mathematics
25 Journal of Fluid Mechanics
24 Acta Mechanica
24 Nonlinear Dynamics
23 Engineering Analysis with Boundary Elements
22 Mathematics and Computers in Simulation
22 Advances in Mathematical Physics
21 Mathematical and Computer Modelling
19 Journal of Computational Physics
19 Physica A
19 Nonlinear Analysis. Real World Applications
18 International Journal of Heat and Mass Transfer
18 International Journal of Computer Mathematics
18 European Journal of Mechanics. B. Fluids
17 Boundary Value Problems
16 Chinese Journal of Physics (Taipei)
15 Journal of Mathematical Chemistry
15 Journal of Applied Mechanics and Technical Physics
15 Advances in Applied Mathematics and Mechanics
14 Computers and Fluids
11 International Journal of Biomathematics
10 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
10 Mathematical Sciences
9 Acta Applicandae Mathematicae
9 Acta Mechanica Sinica
9 International Journal of Differential Equations
8 International Journal of Modern Physics B
8 International Journal of Engineering Science
8 Physics Letters. A
8 Wave Motion
8 Applied Mathematics Letters
8 Journal of the Egyptian Mathematical Society
8 Discrete Dynamics in Nature and Society
8 Journal of Applied Mathematics and Computing
8 Afrika Matematika
7 Computer Physics Communications
7 Journal of Function Spaces
6 Journal of Mathematical Analysis and Applications
6 Applied Numerical Mathematics
6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
6 Fractals
6 Journal of Vibration and Control
6 Asian-European Journal of Mathematics
6 Journal of Mathematics
6 Applied Mathematics and Nonlinear Sciences
5 Journal of the Franklin Institute
5 Mechanics Research Communications
5 Computational Mathematics and Mathematical Physics
5 Filomat
5 Complexity
5 Differential Equations and Dynamical Systems
5 The ANZIAM Journal
5 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences
5 International Journal of Computational Methods
5 Waves in Random and Complex Media
5 International Journal of Structural Stability and Dynamics
5 Palestine Journal of Mathematics
5 Computational Methods for Differential Equations
5 AIMS Mathematics
4 Computer Methods in Applied Mechanics and Engineering
4 Indian Journal of Pure & Applied Mathematics
4 Journal of Mathematical Physics
4 Chaos
4 Mathematical Modelling and Analysis
4 Journal of Systems Science and Complexity
4 Differential Equations & Nonlinear Mechanics
4 Symmetry
4 Arabian Journal for Science and Engineering
4 S\(\vec{\text{e}}\)MA Journal
4 Journal of Computational Methods in Physics
3 Journal of Engineering Mathematics
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Demonstratio Mathematica
3 International Journal for Numerical Methods in Engineering
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Physica D
3 Journal of Scientific Computing
3 Archive of Applied Mechanics
3 Turkish Journal of Mathematics
3 International Journal of Computational Fluid Dynamics
3 International Journal of Nonlinear Sciences and Numerical Simulation
...and 123 more Serials
all top 5

Cited in 43 Fields

752 Fluid mechanics (76-XX)
717 Numerical analysis (65-XX)
472 Partial differential equations (35-XX)
402 Ordinary differential equations (34-XX)
242 Classical thermodynamics, heat transfer (80-XX)
141 Mechanics of deformable solids (74-XX)
124 Biology and other natural sciences (92-XX)
87 Real functions (26-XX)
68 Integral equations (45-XX)
39 Dynamical systems and ergodic theory (37-XX)
36 Mechanics of particles and systems (70-XX)
32 Statistical mechanics, structure of matter (82-XX)
23 Operator theory (47-XX)
23 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
22 Calculus of variations and optimal control; optimization (49-XX)
20 Approximations and expansions (41-XX)
19 Special functions (33-XX)
19 Systems theory; control (93-XX)
17 Probability theory and stochastic processes (60-XX)
15 Integral transforms, operational calculus (44-XX)
14 Computer science (68-XX)
12 Harmonic analysis on Euclidean spaces (42-XX)
11 Optics, electromagnetic theory (78-XX)
11 Quantum theory (81-XX)
9 Astronomy and astrophysics (85-XX)
9 Geophysics (86-XX)
7 Information and communication theory, circuits (94-XX)
6 Statistics (62-XX)
6 Operations research, mathematical programming (90-XX)
4 Algebraic topology (55-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Measure and integration (28-XX)
3 Functional analysis (46-XX)
2 Algebraic geometry (14-XX)
2 Global analysis, analysis on manifolds (58-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Mathematical logic and foundations (03-XX)
1 Combinatorics (05-XX)
1 Field theory and polynomials (12-XX)
1 Functions of a complex variable (30-XX)
1 Sequences, series, summability (40-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.