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: 158 Publications since 1991, including 2 Books 2 Contributions as Editor Co-Authors: 70 Co-Authors with 88 Joint Publications 2,635 Co-Co-Authors all top 5 Co-Authors 62 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 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 2 Zhong, Xiaoxu 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 Gaugler, Trent 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) 58 Numerical analysis (65-XX) 35 Partial differential equations (35-XX) 29 Ordinary differential equations (34-XX) 13 Classical thermodynamics, heat transfer (80-XX) 10 Mechanics of particles and systems (70-XX) 9 Dynamical systems and ergodic theory (37-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 136 Publications have been cited 4,573 times in 1,811 Documents Cited by ▼ Year ▼ On the homotopy analysis method for nonlinear problems. Zbl 1086.35005Liao, Shijun 464 2004 Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001Liao, Shijun 358 2004 Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126Liao, Shijun 245 2009 An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. Zbl 1342.74180Liao, Shi-Jun 195 1999 An approximate solution technique not depending on small parameters: A special example. Zbl 0837.76073Liao, Shijun 191 1995 An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088Liao, Shijun 166 2010 On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Zbl 1063.76671Liao, Shi-Jun 166 2003 A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142Liao, Shijun 161 2005 A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. Zbl 0931.76017Liao, Shijun 161 1999 Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001Liao, Shijun 155 2012 Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534Liao, Shijun 139 2005 A kind of approximation solution technique which does not depend upon small parameters. II: An application in fluid mechanics. Zbl 1031.76542Liao, Shijun 129 1997 Analytic solutions of the temperature distribution in Blasius viscous flow problems. Zbl 1007.76014Liao, Shijun; Campo, Antonio 107 2002 An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022Liao, Shijun 100 2006 Homotopy analysis of nonlinear progressive waves in deep water. Zbl 1112.76316Liao, Shi-Jun; Cheung, Kwok Fai 100 2003 Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008Liao, Shijun; Pop, Ioan 64 2004 Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun 62 2009 A new analytic algorithm of Lane–Emden type equations. Zbl 1022.65078Liao, Shijun 61 2003 An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354Li, Shuicai; Liao, Shi-Jun 57 2005 Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009Wu, Wan; Liao, Shijun 52 2005 Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. Zbl 1195.76069Xu, Hang; Liao, Shi Jun 49 2005 A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046Liao, Shi-Jun 48 2007 Homotopy analysis method: A new analytic method for nonlinear problems. Zbl 1126.34311Liao, Shijun 48 1998 Series solutions of nano boundary layer flows by means of the homotopy analysis method. Zbl 1135.76016Cheng, Jun; Liao, Shijun; Mohapatra, R. N.; Vajravelu, K. 45 2008 Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056Liao, Shijun; Magyari, Eugen 45 2006 An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Zbl 1348.74225Liao, Shi-Jun 40 2003 Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352Liao, Shijun 40 2006 Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method. Zbl 1069.35060Wu, Yongyan; Wang, Chun; Liao, Shi-Jun 39 2005 Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng 38 2009 Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032Abbasbandy, S.; Tan, Y.; Liao, S. J. 38 2007 A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068Liao, Shi-Jun 36 2009 An explicit analytic solution to the Thomas-Fermi equation. Zbl 1034.34005Liao, Shijun 36 2003 An analytic approximation of the drag coefficient for the viscous flow past a sphere. Zbl 1116.76335Liao, Shi-Jun 35 2002 An analytic approximate approach for free oscillations of self-excited systems. Zbl 1348.34071Liao, Shi-Jun 34 2004 Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Zbl 1190.76132Xu, Hang; Lin, Zhi-Liang; Liao, Shi-Jun; Wu, Jie-Zhi; Majdalani, Joseph 34 2010 On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059Yang, Cheng; Liao, Shijun 33 2006 Dual solutions of boundary layer flow over an upstream moving plate. Zbl 1131.35066Xu, 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 1128.74026Wang, Ji; Chen, Jiankang; Liao, Shijun 30 2008 Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Zbl 1105.76061Xu, Hang; Liao, Shijun; Pop, Ioan 29 2007 On the explicit analytic solution of Cheng-Chang equation. Zbl 1029.76050Wang, C.; Zhu, J. M.; Liao, S. J.; Pop, I. 28 2003 Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body. Zbl 1189.76549Liao, Shijun; Su, Jian; Chwang, Allen T. 27 2006 Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313Tan, Yue; Xu, Hang; Liao, Shi-Jun 27 2007 A second-order approximate analytical solution of a simple pendulum by the process analysis method. Zbl 0769.70017Liao, S. J. 27 1992 The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J. 26 2009 Homotopy analysis method: A new analytical technique for nonlinear problems. Zbl 0927.65069Liao, Shijun 26 1997 On the steady-state fully resonant progressive waves in water of finite depth. Zbl 1275.76052Xu, Dali; Lin, Zhiliang; Liao, Shijun; Stiassnie, Michael 25 2012 Numerically solving nonlinear problems by the homotopy analysis method. Zbl 0923.73076Liao, S.-J. 24 1997 An explicit series approximation to the optimal exercise boundary of American put options. Zbl 1221.91053Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun 22 2010 On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206Liao, Shijun 20 2010 On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046Liao, Shi-Jun 20 2011 Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450Liao, Shijun 20 2009 A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 1510.65311Yang, Zhaochen; Liao, Shijun 20 2017 Series solution of unsteady boundary layer flows of non-Newtonian fluids near a forward stagnation point. Zbl 1195.76070Xu, Hang; Liao, Shi Jun; Pop, Ioan 19 2006 An analytical solution for a nonlinear time-delay model in biology. Zbl 1221.65204Khan, Hina; Liao, Shi-Jun; Mohapatra, R. N.; Vajravelu, K. 18 2009 Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Zbl 1311.70031Li, Yajie; Nohara, Ben T.; Liao, Shijun 14 2010 A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 1510.65181Yang, Zhaochen; Liao, Shijun 14 2017 Advances in the homotopy analysis method. Zbl 1283.35003 13 2014 A short note on high-order streamfunction-vorticity formulations of 2D steady state Navier-Stokes equations. Zbl 0873.76052Liao, Shijun; Zhu, Jimao 13 1996 General boundary element method for nonlinear heat transfer problems governed by hyperbolic heat conduction equation. Zbl 0890.65121Liao, S. 12 1997 Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet. Zbl 1186.76616Xu, Hang; Liao, Shi-Jun 12 2009 On the steady-state nearly resonant waves. Zbl 1445.76023Liao, Shijun; Xu, Dali; Stiassnie, Michael 12 2016 On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055Liao, Shijun; Zhao, Yinlong 11 2016 A challenging nonlinear problem for numerical techniques. Zbl 1071.65112Liao, ShiJun 11 2005 Series solutions of unsteady boundary-layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Zbl 1096.76004Xu, H.; Liao, S. J.; Pop, I. 11 2006 An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate. Zbl 0922.34012Liao, Shi-Jun 11 1998 Physical limit of prediction for chaotic motion of three-body problem. Zbl 1473.70019Liao, Shijun 10 2014 Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452Xu, Hang; Liao, Shi-Jun 10 2006 A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falkner-Skan equation. Zbl 0990.76068Liao, Shijun 10 2001 Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations. Zbl 1460.74056Yu, Qiang; Xu, Hang; Liao, Shijun 9 2018 Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach. Zbl 1433.65339Yu, Qiang; Xu, Hang; Liao, Shijun 9 2018 On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007Cheng, Jun; Cang, Jie; Liao, Shijun 9 2009 General boundary element method for nonlinear problems. Zbl 0863.76037Liao, S. J.; Chwang, Allen T. 9 1996 Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. Zbl 1334.80004Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun 9 2014 On the general boundary element method. Zbl 0940.65141Liao, Shijun 9 1998 High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow. Zbl 1452.76137Xie, Bin; Deng, Xi; Liao, ShiJun; Xiao, Feng 8 2019 The scaled boundary FEM for nonlinear problems. Zbl 1221.65305Lin, Zhiliang; Liao, Shijun 8 2011 The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun 8 2012 A family of new solutions on the wall jet. Zbl 1154.76335Xu, Hang; Liao, Shijun; Wu, Guo-Xiong 8 2008 A novel homotopy-wavelet approach for solving stream function-vorticity formulation of Navier-Stokes equations. Zbl 1456.76107Yu, Qiang; Xu, Hang; Liao, Shijun; Yang, Zhaochen 8 2019 An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun 7 2013 Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026Liu, Z.; Xu, D. L.; Liao, S. J. 7 2018 Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292Liu, Y. P.; Liao, S. J.; Li, Z. B. 7 2013 High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. II: Some 2D examples. Zbl 0886.65111Liao, Shijun 7 1997 A direct boundary element approach for unsteady nonlinear heat transfer problems. Zbl 0995.80008Liao, Shijun 7 2002 On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087Yang, Xiaoyan; Dias, Frederic; Liao, Shijun 7 2018 Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nano-fluid. Zbl 1410.76473Farooq, U.; Zhao, Y. L.; Hayat, T.; Alsaedi, A.; Liao, S. J. 7 2015 On the risks of using double precision in numerical simulations of spatio-temporal chaos. Zbl 07506180Hu, Tianli; Liao, Shijun 7 2020 A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids. Zbl 1453.76116Xie, Bin; Jin, Peng; Nakayama, Hiroki; Liao, ShiJun; Xiao, Feng 6 2020 High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. Zbl 0882.65108Liao, Shijun 6 1996 A new method for homoclinic solutions of ordinary differential equations. Zbl 1197.65212Akyildiz, F. Talay; Vajravelu, K.; Liao, S.-J. 6 2009 A new modification of false position method based on homotopy analysis method. Zbl 1231.65084Abbasbandy, Saeid; Liao, Shi-Jun 6 2008 The general boundary element method and its further generalizations. Zbl 0954.76060Liao, Shijun 6 1999 A short note on the general boundary element method for viscous flows with high Reynolds number. Zbl 1055.76037Zhao, X. Y.; Liao, S. J. 6 2003 Analytic solutions of Von Kármán plate under arbitrary uniform pressure – equations in differential form. Zbl 1367.74008Zhong, X. X.; Liao, S. J. 6 2017 Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM. Zbl 1221.76125Lin, Zhiliang; Liao, Shijun 5 2011 Some notes on the general boundary element method for highly nonlinear problems. Zbl 1147.76596Wu, Y. Y.; Liao, S. J.; Zhao, X. Y. 5 2005 The quite general BEM for strongly nonlinear problems. Zbl 0839.65132Liao, S.-J. 5 1995 Influence of numerical noises on computer-generated simulation of spatio-temporal chaos. Zbl 1489.65163Qin, Shijie; Liao, Shijun 5 2020 Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method. Zbl 1065.76152Wu, Yongyan; Liao, Shijun 5 2005 Higher-order streamfunction-vorticity formulation of 2D steady-state Navier-Stokes equations. Zbl 0762.76063Liao, S. J. 4 1992 A kind of Lagrangian chaotic property of the Arnold-Beltrami-Childress flow. Zbl 1520.76036Qin, Shijie; Liao, Shijun 1 2023 Avoiding small denominator problems by means of the homotopy analysis method. Zbl 07646146Liao, Shijun 1 2023 Wave breaking and jet formation on axisymmetric surface gravity waves. Zbl 07465425McAllister, M. L.; Draycott, S.; Davey, T.; Yang, Y.; Adcock, T. A. A.; Liao, S.; van den Bremer, T. S. 2 2022 Ultra-chaos: an insurmountable objective obstacle of reproducibility and replication. Zbl 1499.35445Liao, Shijun; Qin, Shijie 1 2022 Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method. Zbl 07508446Xie, Bin; Deng, Xi; Liao, ShiJun; Xiao, Feng 2 2021 On the risks of using double precision in numerical simulations of spatio-temporal chaos. Zbl 07506180Hu, Tianli; Liao, Shijun 7 2020 A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids. Zbl 1453.76116Xie, Bin; Jin, Peng; Nakayama, Hiroki; Liao, ShiJun; Xiao, Feng 6 2020 Influence of numerical noises on computer-generated simulation of spatio-temporal chaos. Zbl 1489.65163Qin, Shijie; Liao, Shijun 5 2020 High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow. Zbl 1452.76137Xie, Bin; Deng, Xi; Liao, ShiJun; Xiao, Feng 8 2019 A novel homotopy-wavelet approach for solving stream function-vorticity formulation of Navier-Stokes equations. Zbl 1456.76107Yu, Qiang; Xu, Hang; Liao, Shijun; Yang, Zhaochen 8 2019 High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow. Zbl 1442.65208Xie, Bin; Deng, Xi; Liao, Shijun 3 2019 A general analytical approach to study solute dispersion in non-Newtonian fluid flow. Zbl 1475.76088Rana, Jyotirmoy; Liao, Shijun 1 2019 Analytic solutions of the rise dynamics of liquid in a vertical cylindrical capillary. Zbl 1476.76031Zhong, Xiaoxu; Sun, Bohua; Liao, Shijun 1 2019 Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations. Zbl 1460.74056Yu, Qiang; Xu, Hang; Liao, Shijun 9 2018 Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach. Zbl 1433.65339Yu, Qiang; Xu, Hang; Liao, Shijun 9 2018 Finite amplitude steady-state wave groups with multiple near resonances in deep water. Zbl 1421.76026Liu, Z.; Xu, D. L.; Liao, S. J. 7 2018 On the steady-state resonant acoustic-gravity waves. Zbl 1415.76087Yang, Xiaoyan; Dias, Frederic; Liao, Shijun 7 2018 On the generalized wavelet-Galerkin method. Zbl 1377.65098Yang, Zhaochen; Liao, Shijun 4 2018 Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems. Zbl 1404.37094Li, Xiaoming; Liao, Shijun 1 2018 A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. Zbl 1510.65311Yang, Zhaochen; Liao, Shijun 20 2017 A HAM-based wavelet approach for nonlinear ordinary differential equations. Zbl 1510.65181Yang, Zhaochen; Liao, Shijun 14 2017 Analytic solutions of Von Kármán plate under arbitrary uniform pressure – equations in differential form. Zbl 1367.74008Zhong, X. X.; Liao, S. J. 6 2017 On the homotopy analysis method for backward/forward-backward stochastic differential equations. Zbl 1377.65009Zhong, Xiaoxu; Liao, Shijun 2 2017 On the steady-state nearly resonant waves. Zbl 1445.76023Liao, Shijun; Xu, Dali; Stiassnie, Michael 12 2016 On the method of directly defining inverse mapping for nonlinear differential equations. Zbl 1381.65055Liao, Shijun; Zhao, Yinlong 11 2016 Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nano-fluid. Zbl 1410.76473Farooq, U.; Zhao, Y. L.; Hayat, T.; Alsaedi, A.; Liao, S. J. 7 2015 On the inherent self-excited macroscopic randomness of chaotic three-body systems. Zbl 1325.70022Liao, Shijun; Li, Xiaoming 4 2015 Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces. Zbl 1329.76256Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, S. J. 3 2015 A HAM-based analytic approach for physical models with an infinite number of singularities. Zbl 1314.65136Xu, Dali; Cui, Jifeng; Liao, Shijun; Alsaedi, A. 2 2015 Equilibrium states of class-I Bragg resonant wave system. Zbl 1408.76093Xu, 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 1331.65132Yu, 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 1473.70019Liao, Shijun 10 2014 Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. Zbl 1334.80004Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun 9 2014 Can we obtain a reliable convergent chaotic solution in any given finite interval of time? Zbl 1301.34059Liao, Shijun 3 2014 Do peaked solitary water waves indeed exist? Zbl 1457.35057Liao, Shijun 1 2014 HAM-based Mathematica package BVPh 2.0 for nonlinear boundary value problems. Zbl 1301.65082Zhao, Yinlong; Liao, Shijun 1 2014 Phase velocity effects of the wave interaction with exponentially sheared current. Zbl 1456.76022Liu, Zeng; Lin, Zhiliang; Liao, Shijun 1 2014 An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. Zbl 1344.65068Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun 7 2013 Symbolic computation of strongly nonlinear periodic oscillations. Zbl 1325.68292Liu, Y. P.; Liao, S. J.; Li, Z. B. 7 2013 Two new standing solitary waves in shallow water. Zbl 1454.76031Liao, Shijun 1 2013 Homotopy analysis method in nonlinear differential equations. Zbl 1253.35001Liao, Shijun 155 2012 On the steady-state fully resonant progressive waves in water of finite depth. Zbl 1275.76052Xu, Dali; Lin, Zhiliang; Liao, Shijun; Stiassnie, Michael 25 2012 The improved homotopy analysis method for the Thomas-Fermi equation. Zbl 1245.65099Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun 8 2012 A Maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations. Zbl 1255.93054Liu, Yinping; Liao, Shijun; Li, Zhibin 1 2012 On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves. Zbl 1221.76046Liao, Shi-Jun 20 2011 The scaled boundary FEM for nonlinear problems. Zbl 1221.65305Lin, Zhiliang; Liao, Shijun 8 2011 Calculation of added mass coefficients of 3D complicated underwater bodies by FMBEM. Zbl 1221.76125Lin, Zhiliang; Liao, Shijun 5 2011 Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet. Zbl 1206.35208Kousar, Nabeela; Liao, Shijun 2 2011 An optimal homotopy-analysis approach for strongly nonlinear differential equations. Zbl 1222.65088Liao, Shijun 166 2010 Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Zbl 1190.76132Xu, Hang; Lin, Zhi-Liang; Liao, Shi-Jun; Wu, Jie-Zhi; Majdalani, Joseph 34 2010 An explicit series approximation to the optimal exercise boundary of American put options. Zbl 1221.91053Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun 22 2010 On the relationship between the homotopy analysis method and Euler transform. Zbl 1221.65206Liao, Shijun 20 2010 Series solutions of coupled Van der Pol equation by means of homotopy analysis method. Zbl 1311.70031Li, Yajie; Nohara, Ben T.; Liao, Shijun 14 2010 Explicit series solution of a closure model for the von Kármán-Howarth equation. Zbl 1235.34065Liu, Zeng; Oberlack, Martin; Grebenev, Vladimir N.; Liao, Shi-Jun 1 2010 Notes on the homotopy analysis method: some definitions and theorems. Zbl 1221.65126Liao, Shijun 245 2009 Series solutions of non-linear Riccati differential equations with fractional order. Zbl 1197.34006Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun 62 2009 Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Zbl 1221.65286Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng 38 2009 A general approach to get series solution of non-similarity boundary-layer flows. Zbl 1221.76068Liao, Shi-Jun 36 2009 The explicit series solution of SIR and SIS epidemic models. Zbl 1171.92033Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J. 26 2009 Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method. Zbl 1163.35450Liao, Shijun 20 2009 An analytical solution for a nonlinear time-delay model in biology. Zbl 1221.65204Khan, 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 1186.76616Xu, Hang; Liao, Shi-Jun 12 2009 On the interaction of deep water waves and exponential shear currents. Zbl 1173.76007Cheng, Jun; Cang, Jie; Liao, Shijun 9 2009 A new method for homoclinic solutions of ordinary differential equations. Zbl 1197.65212Akyildiz, 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 1196.34027Liao, Shijun 1 2009 Series solutions of nano boundary layer flows by means of the homotopy analysis method. Zbl 1135.76016Cheng, Jun; Liao, Shijun; Mohapatra, R. N.; Vajravelu, K. 45 2008 Dual solutions of boundary layer flow over an upstream moving plate. Zbl 1131.35066Xu, 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 1128.74026Wang, Ji; Chen, Jiankang; Liao, Shijun 30 2008 A family of new solutions on the wall jet. Zbl 1154.76335Xu, Hang; Liao, Shijun; Wu, Guo-Xiong 8 2008 A new modification of false position method based on homotopy analysis method. Zbl 1231.65084Abbasbandy, Saeid; Liao, Shi-Jun 6 2008 A new branch of solutions of boundary-layer flows over a permeable stretching plate. Zbl 1200.76046Liao, Shi-Jun 48 2007 Newton-homotopy analysis method for nonlinear equations. Zbl 1119.65032Abbasbandy, 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 1105.76061Xu, Hang; Liao, Shijun; Pop, Ioan 29 2007 Explicit series solution of travelling waves with a front of Fisher equation. Zbl 1143.35313Tan, Yue; Xu, Hang; Liao, Shi-Jun 27 2007 An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Zbl 1078.76022Liao, Shijun 100 2006 Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. Zbl 1101.76056Liao, Shijun; Magyari, Eugen 45 2006 Series solutions of unsteady boundary-layer flows over a stretching flat plate. Zbl 1145.76352Liao, Shijun 40 2006 On the explicit, purely analytic solution of von Kármán swirling viscous flow. Zbl 1075.35059Yang, Cheng; Liao, Shijun 33 2006 Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body. Zbl 1189.76549Liao, 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 1195.76070Xu, 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 1096.76004Xu, H.; Liao, S. J.; Pop, I. 11 2006 Series solutions of unsteady MHD flows above a rotating disk. Zbl 1163.76452Xu, Hang; Liao, Shi-Jun 10 2006 A series solution of the unsteady von Kármán swirling viscous flows. Zbl 1122.35102Xu, Hang; Liao, Shijun 3 2006 A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Zbl 1189.76142Liao, Shijun 161 2005 Comparison between the homotopy analysis method and homotopy perturbation method. Zbl 1082.65534Liao, Shijun 139 2005 An analytic approach to solve multiple solutions of a strongly nonlinear problem. Zbl 1151.35354Li, Shuicai; Liao, Shi-Jun 57 2005 Solving solitary waves with discontinuity by means of the homotopy analysis method. Zbl 1071.76009Wu, Wan; Liao, Shijun 52 2005 Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. Zbl 1195.76069Xu, Hang; Liao, Shi Jun 49 2005 Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method. Zbl 1069.35060Wu, Yongyan; Wang, Chun; Liao, Shi-Jun 39 2005 A challenging nonlinear problem for numerical techniques. Zbl 1071.65112Liao, ShiJun 11 2005 Some notes on the general boundary element method for highly nonlinear problems. Zbl 1147.76596Wu, Y. Y.; Liao, S. J.; Zhao, X. Y. 5 2005 Solving high Reynolds-number viscous flows by the general BEM and domain decomposition method. Zbl 1065.76152Wu, Yongyan; Liao, Shijun 5 2005 On the homotopy analysis method for nonlinear problems. Zbl 1086.35005Liao, Shijun 464 2004 Beyond perturbation. Introduction to the homotopy analysis method. Zbl 1051.76001Liao, Shijun 358 2004 Explicit analytic solution for similarity boundary layer equations. Zbl 1045.76008Liao, Shijun; Pop, Ioan 64 2004 An analytic approximate approach for free oscillations of self-excited systems. Zbl 1348.34071Liao, Shi-Jun 34 2004 On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. Zbl 1063.76671Liao, Shi-Jun 166 2003 Homotopy analysis of nonlinear progressive waves in deep water. Zbl 1112.76316Liao, Shi-Jun; Cheung, Kwok Fai 100 2003 A new analytic algorithm of Lane–Emden type equations. Zbl 1022.65078Liao, Shijun 61 2003 ...and 36 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,208 Authors 174 Hayat, Tasawar 88 Liao, Shijun 53 Al-saedi, Ahmed Eid Salem 47 Abbasbandy, Saeid 43 Sajid, Muhammad 40 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 Motsa, Sandile Sydney 24 Kumar, Devendra 23 Abbas, Zaheer 21 Noorani, Mohd Salmi Mohd 20 Alomari, Abedel-Karrem 20 Singh, Jagdev 19 Shehzad, Sabir Ali 18 Zheng, Liancun 16 Ellahi, Rahmat 16 Nazar, Roslinda Mohd 16 Odibat, Zaid M. 16 Sibanda, Precious 16 Veeresha, Pundikala 15 Dinarvand, Saeed 15 Fang, Tiegang 14 Ayub, Muhammad 14 Mustafa, Meraj 14 Nadeem, Sohail 14 Prakasha, Doddabhadrappla Gowda 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 de la Sen, Manuel 10 Jafari, Hossein 10 Parand, Kourosh 9 Akinyemi, Lanre 9 Alonso Quesada, Santiago 9 Awais, Muhammad 9 Baskonus, Haci Mehmet 9 Gómez-Aguilar, José Francisco 9 Ibeas, Asier 9 Ishak, Anuar 9 Muhammad, Taseer 9 Obaidat, Saleem A. 9 Ramos, Juan I. 9 Roul, Pradip 9 Shivanian, Elyas 9 Xie, Bin 8 He, Jihuan 8 Lin, Zhiliang 8 Liu, Zeng 8 Si, Xinhui 8 Yu, Qiang 7 Ariel, P. Donald 7 Awawdeh, Fadi 7 Bararnia, H. 7 Dewasurendra, Mangalagama 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 Imtiaz, Maria 6 Januário, Cristina 6 Khan, Ilyas 6 Khan, Masood Amjad 6 Kimiaeifar, A. 6 Kumaran, Vishwanathan 6 Li, Lin 6 Liang, Songxin 6 Mohyud-Din, Syed Tauseef 6 Noor, Muhammad Aslam 6 Qian, Youhua 6 Rabbani, Mohsen 6 Srivastava, Hari Mohan 6 Syam, Muhammed I. 6 Vázquez-Leal, Héctor 6 Wu, Yongyan ...and 2,108 more Authors all top 5 Cited in 213 Serials 150 Communications in Nonlinear Science and Numerical Simulation 134 Applied Mathematics and Computation 69 Mathematical Problems in Engineering 58 Chaos, Solitons and Fractals 54 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) 32 AMM. Applied Mathematics and Mechanics. (English Edition) 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 Mathematical Methods in the Applied Sciences 26 Numerical Methods for Partial Differential Equations 26 Computational and Applied Mathematics 23 Acta Mechanica 23 Nonlinear Dynamics 22 Journal of Fluid Mechanics 22 Mathematics and Computers in Simulation 22 Engineering Analysis with Boundary Elements 22 Advances in Mathematical Physics 21 Mathematical and Computer Modelling 19 Physica A 19 Nonlinear Analysis. Real World Applications 18 International Journal of Heat and Mass Transfer 18 Journal of Computational Physics 18 International Journal of Computer Mathematics 17 European Journal of Mechanics. B. Fluids 17 Boundary Value Problems 15 Journal of Applied Mechanics and Technical Physics 14 Journal of Mathematical Chemistry 13 Computers and Fluids 11 International Journal of Biomathematics 10 Advances in Applied Mathematics and Mechanics 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 Journal of Function Spaces 6 Computer Physics Communications 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 AIMS Mathematics 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 4 Computational Methods for Differential Equations 3 Computer Methods in Applied Mechanics and Engineering 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Demonstratio Mathematica 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Physica D 3 Archive of Applied Mechanics 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 The Journal of Prime Research in Mathematics 3 International Journal for Numerical Methods in Biomedical Engineering 3 Mathematics 3 Journal of Linear and Topological Algebra 2 Applicable Analysis 2 Journal of Engineering Mathematics ...and 113 more Serials all top 5 Cited in 44 Fields 715 Fluid mechanics (76-XX) 691 Numerical analysis (65-XX) 443 Partial differential equations (35-XX) 391 Ordinary differential equations (34-XX) 226 Classical thermodynamics, heat transfer (80-XX) 137 Mechanics of deformable solids (74-XX) 117 Biology and other natural sciences (92-XX) 87 Real functions (26-XX) 66 Integral equations (45-XX) 37 Dynamical systems and ergodic theory (37-XX) 33 Statistical mechanics, structure of matter (82-XX) 32 Mechanics of particles and systems (70-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 21 Operator theory (47-XX) 19 Approximations and expansions (41-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 18 Special functions (33-XX) 17 Systems theory; control (93-XX) 15 Probability theory and stochastic processes (60-XX) 14 Integral transforms, operational calculus (44-XX) 13 Computer science (68-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Quantum theory (81-XX) 9 Astronomy and astrophysics (85-XX) 8 Optics, electromagnetic theory (78-XX) 8 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 Difference and functional equations (39-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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