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, Shi Jun; Liao, S.-J.; Liao, S. more...less External Links: Wikidata · GND · IdRef Documents Indexed: 160 Publications since 1991, including 3 Books and 1 Additional arXiv Preprint 2 Contributions as Editor Co-Authors: 70 Co-Authors with 89 Joint Publications 2,664 Co-Co-Authors all top 5 Co-Authors 63 single-authored 16 Xu, Hang 8 Lin, Zhiliang 6 Liu, Zeng 5 Pop, Ioan 5 Xie, Bin 5 Xu, Dali 5 Zhao, Yinlong 5 Zhu, Jimao 4 Al-saedi, Ahmed Eid Salem 4 Qin, Shijie 4 Vajravelu, Kuppalapalle 4 Wang, Chun 4 Yang, Zhaochen 3 Cheng, Jun 3 Chwang, Allen Tseyung 3 Deng, Xi 3 Hayat, Tasawar 3 Li, Xiaoming 3 Mohapatra, Ram Narayan 3 Tan, Yue 3 Xiao, Feng 3 Yu, Qiang 3 Zhong, Xiaoxu 2 Abbasbandy, Saeid 2 Cang, Jie 2 Dias, Frédéric 2 Khan, Hina 2 Li, Rong-Kwei 2 Li, Xiaochen 2 Li, Zhibin 2 Liu, Yinping 2 Stiassnie, Michael Aharon 2 Wu, Yongyan 2 Yang, Xiaoyan 2 Yang, Yu 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 Kim, Daeyoung 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 Wang, L. 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 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) all top 5 Fields 82 Fluid mechanics (76-XX) 59 Numerical analysis (65-XX) 35 Partial differential equations (35-XX) 29 Ordinary differential equations (34-XX) 13 Classical thermodynamics, heat transfer (80-XX) 10 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 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) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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