Edit Profile (opens in new tab) Liao, Shijun Co-Author Distance Author ID: liao.shijun Published as: Liao, Shijun; Liao, Shi-Jun; Liao, S. J.; Liao, ShiJun; Liao, S.-J.; Liao, S.; Liao, Shi Jun more...less Homepage: https://numericaltank.sjtu.edu.cn/ External Links: Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef Documents Indexed: 158 Publications since 1991, including 3 Books and 1 Additional arXiv Preprint 2 Contributions as Editor Software Indexed: 2 Packages Co-Authors: 73 Co-Authors with 95 Joint Publications 2,806 Co-Co-Authors all top 5 Co-Authors 63 single-authored 16 Xu, Hang 8 Lin, Zhiliang 6 Liu, Zeng 6 Qin, Shijie 5 Pop, Ioan 5 Xie, Bin 5 Xu, Dali 5 Zhao, Yinlong 5 Zhu, Jimao 4 Al-saedi, Ahmed Eid Salem 4 Tan, Yue 4 Vajravelu, Kuppalapalle 4 Wang, Chun 4 Yang, Zhaochen 4 Zhong, Xiaoxu 3 Cheng, Jun 3 Chwang, Allen Tseyung 3 Deng, Xi 3 Hayat, Tasawar 3 Li, Xiaoming 3 Mohapatra, Ram Narayan 3 Wu, Yongyan 3 Xiao, Feng 3 Yang, Yu 3 Yu, Qiang 2 Abbasbandy, Saeid 2 Cang, Jie 2 Dias, Frédéric 2 Khan, Hina 2 Li, Xiaochen 2 Li, Zhibin 2 Liu, Yinping 2 Stiassnie, Michael Aharon 2 Yang, Xiaoyan 1 Adcock, Thomas A. A. 1 Borthwick, Alistair G. L. 1 Campo, Antonio 1 Chang, Chueh-Hsin 1 Chen, Jiankang 1 Cheung, Kwok Fai 1 Cui, Jifeng 1 Draycott, Samuel 1 Grebenev, Vladimir N. 1 He, Linghui 1 Hu, Tianli 1 Jin, Peng 1 Kousar, Nabeela 1 Li, Jing 1 Li, Jiyang 1 Li, Shuicai 1 Li, Yajie 1 Magyari, Eugen 1 Majdalani, Joseph 1 Mashayek, Farzad 1 McAllister, M. Luisa N. 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 Van Den Bremer, Ton S. 1 Wang, Ji 1 Wu, Guo Xiong 1 Wu, Jiezhi 1 Wu, Wan 1 Xu, Tianzhuang 1 Yang, Cheng 1 You, Xiangcheng 1 Yu, Ching-Hao 1 Zhu, Songping 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 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Computational and Applied Mathematics 3 Studies in Applied Mathematics 3 Applied Mathematics and Mechanics. (English Edition) 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 Physica D 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 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematical Modelling 1 Celestial Mechanics and Dynamical Astronomy 1 Physics of Fluids 1 Journal of Systems Science and Complexity 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Advances in Applied Mathematics (Boca Raton) all top 5 Fields 82 Fluid mechanics (76-XX) 59 Numerical analysis (65-XX) 35 Partial differential equations (35-XX) 30 Ordinary differential equations (34-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Dynamical systems and ergodic theory (37-XX) 10 Mechanics of particles and systems (70-XX) 8 Mechanics of deformable solids (74-XX) 3 Real functions (26-XX) 3 Approximations and expansions (41-XX) 3 Computer science (68-XX) 2 Operator theory (47-XX) 2 Optics, electromagnetic theory (78-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 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 147 Publications have been cited 5,614 times in 2,159 Documents Cited by ▼ Year ▼ On the homotopy analysis method for nonlinear problems. Zbl 1086.35005 Liao, Shijun 552 2004 Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001 Liao, Shijun 390 2004 Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126 Liao, Shijun 265 2009 An approximate solution technique not depending on small parameters: A special example. Zbl 0837.76073 Liao, Shijun 235 1995 Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001 Liao, Shijun 234 2012 An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. Zbl 1342.74180 Liao, Shi-Jun 231 1999 On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Zbl 1063.76671 Liao, Shi-Jun 202 2003 An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088 Liao, Shijun 199 2010 A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142 Liao, Shijun 192 2005 A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. Zbl 0931.76017 Liao, Shijun 177 1999 Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534 Liao, Shijun 172 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 145 1997 A general approach to obtain series solutions of nonlinear differential equations. Zbl 1533.34017 Liao, S.; Tan, Y. 135 2007 Analytic solutions of the temperature distribution in Blasius viscous flow problems. Zbl 1007.76014 Liao, Shijun; Campo, Antonio 116 2002 An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022 Liao, Shijun 115 2006 Homotopy analysis of nonlinear progressive waves in deep water. Zbl 1112.76316 Liao, Shi-Jun; Cheung, Kwok Fai 112 2003 Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008 Liao, Shijun; Pop, Ioan 76 2004 A new analytic algorithm of Lane–Emden type equations. Zbl 1022.65078 Liao, Shijun 71 2003 Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006 Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun 69 2009 An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354 Li, Shuicai; Liao, Shi-Jun 63 2005 Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009 Wu, Wan; Liao, Shijun 63 2005 Homotopy analysis method: A new analytic method for nonlinear problems. Zbl 1126.34311 Liao, Shijun 59 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 56 2005 A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046 Liao, Shi-Jun 51 2007 Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056 Liao, Shijun; Magyari, Eugen 51 2006 Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352 Liao, Shijun 50 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. 47 2008 An explicit analytic solution to the Thomas-Fermi equation. Zbl 1034.34005 Liao, Shijun 46 2003 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 43 2005 An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Zbl 1348.74225 Liao, Shi-Jun 43 2003 Homotopy analysis method: A new analytical technique for nonlinear problems. Zbl 0927.65069 Liao, Shijun 41 1997 A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068 Liao, Shi-Jun 40 2009 On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059 Yang, Cheng; Liao, Shijun 40 2006 Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286 Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng 39 2009 Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032 Abbasbandy, S.; Tan, Y.; Liao, S. J. 38 2007 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 37 2010 An analytic approximation of the drag coefficient for the viscous flow past a sphere. Zbl 1116.76335 Liao, Shi-Jun 37 2002 An analytic approximate approach for free oscillations of self-excited systems. Zbl 1348.34071 Liao, Shi-Jun 37 2004 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 34 2007 Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313 Tan, Yue; Xu, Hang; Liao, Shi-Jun 33 2007 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 32 2008 On the explicit analytic solution of Cheng-Chang equation. Zbl 1029.76050 Wang, C.; Zhu, J. M.; Liao, S. J.; Pop, I. 29 2003 A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 1510.65311 Yang, Zhaochen; Liao, Shijun 29 2017 The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033 Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J. 29 2009 A second-order approximate analytical solution of a simple pendulum by the process analysis method. Zbl 0769.70017 Liao, S. J. 27 1992 On the steady-state fully resonant progressive waves in water of finite depth. Zbl 1275.76052 Xu, Dali; Lin, Zhiliang; Liao, Shijun; Stiassnie, Michael 27 2012 Numerically solving nonlinear problems by the homotopy analysis method. Zbl 0923.73076 Liao, S.-J. 27 1997 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 A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 1510.65181 Yang, Zhaochen; Liao, Shijun 24 2017 Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450 Liao, Shijun 24 2009 An explicit series approximation to the optimal exercise boundary of American put options. Zbl 1221.91053 Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun 23 2010 On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206 Liao, Shijun 22 2010 An analytical solution for a nonlinear time-delay model in biology. Zbl 1221.65204 Khan, Hina; Liao, Shi-Jun; Mohapatra, R. N.; Vajravelu, K. 21 2009 On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046 Liao, Shi-Jun 21 2011 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 21 2006 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 18 2019 Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Zbl 1311.70031 Li, Yajie; Nohara, Ben T.; Liao, Shijun 16 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 16 2009 On the steady-state nearly resonant waves. Zbl 1445.76023 Liao, Shijun; Xu, Dali; Stiassnie, Michael 15 2016 On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055 Liao, Shijun; Zhao, Yinlong 15 2016 A short note on high-order streamfunction-vorticity formulations of 2D steady state Navier-Stokes equations. Zbl 0873.76052 Liao, Shijun; Zhu, Jimao 14 1996 Advances in the homotopy analysis method. Zbl 1283.35003 14 2014 An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate. Zbl 0922.34012 Liao, Shi-Jun 14 1998 A simple approach of enlarging convergence regions of perturbation approximations. Zbl 0949.70003 Liao, Shijun 13 1999 General boundary element method for nonlinear heat transfer problems governed by hyperbolic heat conduction equation. Zbl 0890.65121 Liao, S. 13 1997 Physical limit of prediction for chaotic motion of three-body problem. Zbl 1473.70019 Liao, Shijun 13 2014 An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068 Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun 12 2013 A challenging nonlinear problem for numerical techniques. Zbl 1071.65112 Liao, ShiJun 12 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 12 2014 Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452 Xu, Hang; Liao, Shi-Jun 12 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. 12 2006 A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falkner-Skan equation. Zbl 0990.76068 Liao, Shijun 11 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 11 2018 The scaled boundary FEM for nonlinear problems. Zbl 1221.65305 Lin, Zhiliang; Liao, Shijun 10 2011 General boundary element method for nonlinear problems. Zbl 0863.76037 Liao, S. J.; Chwang, Allen T. 10 1996 The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099 Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun 10 2012 A family of new solutions on the wall jet. Zbl 1154.76335 Xu, Hang; Liao, Shijun; Wu, Guo-Xiong 10 2008 On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007 Cheng, Jun; Cang, Jie; Liao, Shijun 10 2009 On the risks of using double precision in numerical simulations of spatio-temporal chaos. Zbl 07506180 Hu, Tianli; Liao, Shijun 9 2020 On the general boundary element method. Zbl 0940.65141 Liao, Shijun 9 1998 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 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 9 2020 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. 9 2015 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 Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292 Liu, Y. P.; Liao, S. J.; Li, Z. B. 8 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. 8 2015 On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087 Yang, Xiaoyan; Dias, Frederic; Liao, Shijun 8 2018 Influence of numerical noises on computer-generated simulation of spatio-temporal chaos. Zbl 1489.65163 Qin, Shijie; Liao, Shijun 7 2020 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 High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. Zbl 0882.65108 Liao, Shijun 7 1996 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 direct boundary element approach for unsteady nonlinear heat transfer problems. Zbl 0995.80008 Liao, Shijun 7 2002 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. 7 2003 The general boundary element method and its further generalizations. Zbl 0954.76060 Liao, Shijun 7 1999 A new modification of false position method based on homotopy analysis method. Zbl 1231.65084 Abbasbandy, Saeid; Liao, Shi-Jun 7 2008 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 The quite general BEM for strongly nonlinear problems. Zbl 0839.65132 Liao, S.-J. 6 1995 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. 6 2005 Clean numerical simulation. Zbl 07775702 Liao, Shijun 1 2024 A kind of Lagrangian chaotic property of the Arnold-Beltrami-Childress flow. Zbl 1520.76036 Qin, Shijie; Liao, Shijun 4 2023 Avoiding small denominator problems by means of the homotopy analysis method. Zbl 1524.65301 Liao, Shijun 1 2023 Ultra-chaos in a meandering jet flow. Zbl 1536.76050 Zhang, Bo; Liao, Shijun 1 2023 A self-adaptive algorithm of the clean numerical simulation (CNS) for chaos. Zbl 1524.65951 Qin, Shijie; Liao, Shijun 1 2023 Ultra-chaos: an insurmountable objective obstacle of reproducibility and replication. Zbl 1499.35445 Liao, Shijun; Qin, Shijie 3 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. 3 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 2 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 9 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 9 2020 Influence of numerical noises on computer-generated simulation of spatio-temporal chaos. Zbl 1489.65163 Qin, Shijie; Liao, Shijun 7 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 18 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 5 2019 A general analytical approach to study solute dispersion in non-Newtonian fluid flow. Zbl 1475.76088 Rana, Jyotirmoy; Liao, Shijun 2 2019 Stability and hysteresis of Faraday waves in Hele-Shaw cells. Zbl 1419.76225 Li, Jing; Li, Xiaochen; Liao, Shijun 2 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 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 11 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 29 2017 A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 1510.65181 Yang, Zhaochen; Liao, Shijun 24 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 15 2016 On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055 Liao, Shijun; Zhao, Yinlong 15 2016 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. 9 2015 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. 8 2015 On the inherent self-excited macroscopic randomness of chaotic three-body systems. Zbl 1325.70022 Liao, Shijun; Li, Xiaoming 6 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 14 2014 Physical limit of prediction for chaotic motion of three-body problem. Zbl 1473.70019 Liao, Shijun 13 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 12 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 2 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 12 2013 Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292 Liu, Y. P.; Liao, S. J.; Li, Z. B. 8 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 234 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 27 2012 The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099 Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun 10 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 21 2011 The scaled boundary FEM for nonlinear problems. Zbl 1221.65305 Lin, Zhiliang; Liao, Shijun 10 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 199 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 37 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 23 2010 On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206 Liao, Shijun 22 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 16 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 265 2009 Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006 Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun 69 2009 A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068 Liao, Shi-Jun 40 2009 Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286 Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng 39 2009 The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033 Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J. 29 2009 Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450 Liao, Shijun 24 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. 21 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 16 2009 On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007 Cheng, Jun; Cang, Jie; Liao, Shijun 10 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. 47 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 32 2008 A family of new solutions on the wall jet. Zbl 1154.76335 Xu, Hang; Liao, Shijun; Wu, Guo-Xiong 10 2008 A new modification of false position method based on homotopy analysis method. Zbl 1231.65084 Abbasbandy, Saeid; Liao, Shi-Jun 7 2008 A general approach to obtain series solutions of nonlinear differential equations. Zbl 1533.34017 Liao, S.; Tan, Y. 135 2007 A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046 Liao, Shi-Jun 51 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 34 2007 Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313 Tan, Yue; Xu, Hang; Liao, Shi-Jun 33 2007 A short communication on Dr. He’s modified Lindstedt-Poincaré method. Zbl 1181.70003 Liao, Shijun 1 2007 An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022 Liao, Shijun 115 2006 Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056 Liao, Shijun; Magyari, Eugen 51 2006 Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352 Liao, Shijun 50 2006 On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059 Yang, Cheng; Liao, Shijun 40 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 21 2006 Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452 Xu, Hang; Liao, Shi-Jun 12 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. 12 2006 A series solution of the unsteady von Kármán swirling viscous flows. Zbl 1122.35102 Xu, Hang; Liao, Shijun 4 2006 A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142 Liao, Shijun 192 2005 Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534 Liao, Shijun 172 2005 An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354 Li, Shuicai; Liao, Shi-Jun 63 2005 Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009 Wu, Wan; Liao, Shijun 63 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 56 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 43 2005 A challenging nonlinear problem for numerical techniques. Zbl 1071.65112 Liao, ShiJun 12 2005 ...and 47 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,725 Authors 199 Hayat, Tasawar 100 Liao, Shijun 67 Al-saedi, Ahmed Eid Salem 51 Abbasbandy, Saeid 49 Sajid, Muhammad 48 Xu, Hang 44 Ganji, Davood Domiri 42 Vajravelu, Kuppalapalle 41 Băleanu, Dumitru I. 39 Pop, Ioan 35 van Gorder, Robert Ashton 32 Hashim, Ishak 30 Asghar, Saleem 29 Abbas, Zaheer 29 Kumar, Devendra 27 Rashidi, Mohammad Mehdi 25 Motsa, Sandile Sydney 24 Noorani, Mohd Salmi Mohd 24 Singh, Jagdev 22 Alomari, Abedel-Karrem 22 Shehzad, Sabir Ali 21 Veeresha, Pundikala 20 Muhammad, Taseer 19 Nadeem, Sohail 19 Prakasha, Doddabhadrappla Gowda 19 Zheng, Liancun 18 Odibat, Zaid M. 17 Ayub, Muhammad 16 Ellahi, Rahmat 16 Nazar, Roslinda Mohd 16 Sibanda, Precious 15 Bataineh, Ahmad Sami 15 Dehghan Takht Fooladi, Mehdi 15 Dinarvand, Saeed 15 Fang, Tiegang 15 Islam, Saeed 15 Javed, Tariq 15 Turkyilmazoglu, Mustafa 14 Kiliçman, Adem 14 Kumar, Sunil 14 Shateyi, Stanford 14 Yıldırım, Ahmet 13 He, Ji-Huan 13 Saad, Khaled Mohammed 13 Zhang, Xinxin 12 Awais, Muhammad 12 Momani, Shaher M. 12 Mustafa, Meraj 12 Parand, Kourosh 12 Roul, Pradip 11 Akinyemi, Lanre 11 Inc, Mustafa 11 Khan, Masood 10 Baskonus, Haci Mehmet 10 Chen, Yanmao 10 de la Sen, Manuel 10 Gómez-Aguilar, José Francisco 10 Jafari, Hossein 10 Lin, Zhiliang 10 Xie, Bin 10 Yu, Qiang 9 Alonso Quesada, Santiago 9 Ibeas, Asier 9 Ishak, Anuar 9 Liu, Jike 9 Molabahrami, Ahmad 9 Obaidat, Saleem A. 9 Ramos, Juan I. 9 Shidfar, Abdollah 9 Shivanian, Elyas 9 Si, Xinhui 8 Dewasurendra, Mangalagama 8 Khan, Yasir 8 Kumar, Amit 8 Liu, Zeng 8 Singh, Randhir 8 Song, Lina 8 Xiao, Feng 7 Ali, Nasir 7 Ariel, P. Donald 7 Awawdeh, Fadi 7 Bararnia, H. 7 Imtiaz, Maria 7 Iyiola, Olaniyi Samuel 7 Khan, Noor Saeed 7 Li, Lin 7 Liang, Songxin 7 Naz, Rahila 7 Qasim, Muhammad 7 Srivastava, Hari Mohan 7 Syam, Muhammed I. 7 Wang, Ping 7 Wu, Yongyan 7 Zhang, Ji 7 Zou, Li 6 Abdulaziz, O. 6 Agarwal, Ravi P. 6 Al-Mdallal, Qasem M. 6 Babolian, Esmail 6 Biazar, Jafar ...and 2,625 more Authors all top 5 Cited in 237 Serials 167 Communications in Nonlinear Science and Numerical Simulation 144 Applied Mathematics and Computation 72 Mathematical Problems in Engineering 61 Computers & Mathematics with Applications 61 Chaos, Solitons and Fractals 56 Applied Mathematical Modelling 55 Mathematical Methods in the Applied Sciences 55 Physics Letters. 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Section A. Physical Sciences 5 International Journal of Computational Methods 5 Waves in Random and Complex Media 5 AIMS Mathematics 4 Indian Journal of Pure & Applied Mathematics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Journal of the Nigerian Mathematical Society 4 Applied Mathematics. Series B (English Edition) 4 Journal of Systems Science and Complexity 4 Differential Equations & Nonlinear Mechanics 4 Communications in Theoretical Physics 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 Demonstratio Mathematica 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Studies in Applied Mathematics ...and 137 more Serials all top 5 Cited in 44 Fields 855 Fluid mechanics (76-XX) 839 Numerical analysis (65-XX) 563 Partial differential equations (35-XX) 452 Ordinary differential equations (34-XX) 288 Classical thermodynamics, heat transfer (80-XX) 160 Mechanics of deformable solids (74-XX) 131 Biology and other natural sciences (92-XX) 101 Real functions (26-XX) 72 Integral equations (45-XX) 47 Dynamical systems and ergodic theory (37-XX) 41 Mechanics of particles and systems (70-XX) 36 Statistical mechanics, structure of matter (82-XX) 28 Approximations and expansions (41-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 27 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Probability theory and stochastic processes (60-XX) 22 Operator theory (47-XX) 21 Special functions (33-XX) 21 Integral transforms, operational calculus (44-XX) 19 Computer science (68-XX) 18 Systems theory; control (93-XX) 17 Quantum theory (81-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 11 Optics, electromagnetic theory (78-XX) 11 Astronomy and astrophysics (85-XX) 11 Geophysics (86-XX) 8 Information and communication theory, circuits (94-XX) 6 Statistics (62-XX) 5 Operations research, mathematical programming (90-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Algebraic topology (55-XX) 3 Measure and integration (28-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Relativity and gravitational theory (83-XX) 2 Algebraic geometry (14-XX) 2 Functions of a complex variable (30-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 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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