Liao, Shijun Avoiding small denominator problems by means of the homotopy analysis method. (English) Zbl 1524.65301 Adv. Appl. Math. Mech. 15, No. 2, 267-299 (2023). MSC: 65L99 34A25 34C25 41A58 PDFBibTeX XMLCite \textit{S. Liao}, Adv. Appl. Math. Mech. 15, No. 2, 267--299 (2023; Zbl 1524.65301) Full Text: DOI arXiv
Yang, Xiaoyan; Dias, Frederic; Liu, Zeng; Liao, Shijun Finite-amplitude steady-state resonant waves in a circular basin. (English) Zbl 1497.76017 J. Fluid Mech. 915, Paper No. A136, 24 p. (2021). MSC: 76B15 76B07 76M99 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Fluid Mech. 915, Paper No. A136, 24 p. (2021; Zbl 1497.76017) Full Text: DOI
Zhong, Xiaoxu; Sun, Bohua; Liao, Shijun Analytic solutions of the rise dynamics of liquid in a vertical cylindrical capillary. (English) Zbl 1476.76031 Eur. J. Mech., B, Fluids 78, 1-10 (2019). MSC: 76D45 76M45 PDFBibTeX XMLCite \textit{X. Zhong} et al., Eur. J. Mech., B, Fluids 78, 1--10 (2019; Zbl 1476.76031) Full Text: DOI arXiv
Rana, Jyotirmoy; Liao, Shijun A general analytical approach to study solute dispersion in non-Newtonian fluid flow. (English) Zbl 1475.76088 Eur. J. Mech., B, Fluids 77, 183-200 (2019). MSC: 76R99 76A05 76V05 76Z05 76M45 PDFBibTeX XMLCite \textit{J. Rana} and \textit{S. Liao}, Eur. J. Mech., B, Fluids 77, 183--200 (2019; Zbl 1475.76088) Full Text: DOI
Yu, Qiang; Xu, Hang; Liao, Shijun Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations. (English) Zbl 1460.74056 Appl. Math. Modelling 61, 316-340 (2018). MSC: 74K20 74S99 PDFBibTeX XMLCite \textit{Q. Yu} et al., Appl. Math. Modelling 61, 316--340 (2018; Zbl 1460.74056) Full Text: DOI
Yang, Zhaochen; Liao, Shijun A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application. (English) Zbl 1510.65311 Commun. Nonlinear Sci. Numer. Simul. 53, 249-262 (2017). MSC: 65N99 65T60 PDFBibTeX XMLCite \textit{Z. Yang} and \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 53, 249--262 (2017; Zbl 1510.65311) Full Text: DOI
Yang, Zhaochen; Liao, Shijun A HAM-based wavelet approach for nonlinear ordinary differential equations. (English) Zbl 1510.65181 Commun. Nonlinear Sci. Numer. Simul. 48, 439-453 (2017). MSC: 65L99 34A45 PDFBibTeX XMLCite \textit{Z. Yang} and \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 48, 439--453 (2017; Zbl 1510.65181) Full Text: DOI
Zhong, Xiaoxu; Liao, Shijun On the homotopy analysis method for backward/forward-backward stochastic differential equations. (English) Zbl 1377.65009 Numer. Algorithms 76, No. 2, 487-519 (2017). MSC: 65C30 60H10 60H35 34F05 65Y20 PDFBibTeX XMLCite \textit{X. Zhong} and \textit{S. Liao}, Numer. Algorithms 76, No. 2, 487--519 (2017; Zbl 1377.65009) Full Text: DOI arXiv
Liao, Shijun; Zhao, Yinlong On the method of directly defining inverse mapping for nonlinear differential equations. (English) Zbl 1381.65055 Numer. Algorithms 72, No. 4, 989-1020 (2016). Reviewer: Johannes Schropp (Konstanz) MSC: 65L09 65L10 34A55 34B15 PDFBibTeX XMLCite \textit{S. Liao} and \textit{Y. Zhao}, Numer. Algorithms 72, No. 4, 989--1020 (2016; Zbl 1381.65055) Full Text: DOI arXiv
Xu, Dali; Lin, Zhiliang; Liao, Shijun Equilibrium states of class-I Bragg resonant wave system. (English) Zbl 1408.76093 Eur. J. Mech., B, Fluids 50, 38-51 (2015). MSC: 76B15 76M25 PDFBibTeX XMLCite \textit{D. Xu} et al., Eur. J. Mech., B, Fluids 50, 38--51 (2015; Zbl 1408.76093) Full Text: DOI
Farooq, U.; Zhao, Y. L.; Hayat, T.; Alsaedi, A.; Liao, S. J. Application of the HAM-based Mathematica package BVPh 2.0 on MHD Falkner-Skan flow of nano-fluid. (English) Zbl 1410.76473 Comput. Fluids 111, 69-75 (2015). MSC: 76W05 76M25 76D10 80A20 PDFBibTeX XMLCite \textit{U. Farooq} et al., Comput. Fluids 111, 69--75 (2015; Zbl 1410.76473) Full Text: DOI
Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, S. J. Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces. (English) Zbl 1329.76256 Numer. Algorithms 70, No. 1, 43-59 (2015). MSC: 76M25 76D10 76T20 PDFBibTeX XMLCite \textit{U. Farooq} et al., Numer. Algorithms 70, No. 1, 43--59 (2015; Zbl 1329.76256) Full Text: DOI
Xu, Dali; Cui, Jifeng; Liao, Shijun; Alsaedi, A. A HAM-based analytic approach for physical models with an infinite number of singularities. (English) Zbl 1314.65136 Numer. Algorithms 69, No. 1, 59-74 (2015). MSC: 65M99 35Q53 PDFBibTeX XMLCite \textit{D. Xu} et al., Numer. Algorithms 69, No. 1, 59--74 (2015; Zbl 1314.65136) Full Text: DOI
Liao, Shijun Do peaked solitary water waves indeed exist? (English) Zbl 1457.35057 Commun. Nonlinear Sci. Numer. Simul. 19, No. 6, 1792-1821 (2014). MSC: 35Q53 35A30 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 19, No. 6, 1792--1821 (2014; Zbl 1457.35057) Full Text: DOI arXiv
Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. (English) Zbl 1334.80004 Appl. Math. Comput. 242, 528-540 (2014). MSC: 80A20 76A05 82D80 PDFBibTeX XMLCite \textit{U. Farooq} et al., Appl. Math. Comput. 242, 528--540 (2014; Zbl 1334.80004) Full Text: DOI
Zhao, Yinlong; Liao, Shijun HAM-based Mathematica package BVPh 2.0 for nonlinear boundary value problems. (English) Zbl 1301.65082 Liao, Shijun (ed.), Advances in the homotopy analysis method. Hackensack, NJ: World Scientific (ISBN 978-981-4551-24-3/hbk; 978-981-4551-26-7/ebook). 361-417 (2014). MSC: 65L10 34B15 65Y15 65L15 PDFBibTeX XMLCite \textit{Y. Zhao} and \textit{S. Liao}, in: Advances in the homotopy analysis method. Hackensack, NJ: World Scientific. 361--417 (2014; Zbl 1301.65082)
Liao, Shijun Chance and challenge: a brief review of homotopy analysis method. (English) Zbl 1301.65039 Liao, Shijun (ed.), Advances in the homotopy analysis method. Hackensack, NJ: World Scientific (ISBN 978-981-4551-24-3/hbk; 978-981-4551-26-7/ebook). 1-33 (2014). MSC: 65J15 47J25 65L05 65P20 76D05 76B15 34A34 70F07 65M70 PDFBibTeX XMLCite \textit{S. Liao}, in: Advances in the homotopy analysis method. Hackensack, NJ: World Scientific. 1--33 (2014; Zbl 1301.65039)
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. (English) Zbl 1344.65068 Comput. Phys. Commun. 184, No. 9, 2136-2144 (2013). MSC: 65L10 PDFBibTeX XMLCite \textit{Y. Zhao} et al., Comput. Phys. Commun. 184, No. 9, 2136--2144 (2013; Zbl 1344.65068) Full Text: DOI
Liu, Y. P.; Liao, S. J.; Li, Z. B. Symbolic computation of strongly nonlinear periodic oscillations. (English) Zbl 1325.68292 J. Symb. Comput. 55, 72-95 (2013). MSC: 68W30 65L99 68T15 34C15 PDFBibTeX XMLCite \textit{Y. P. Liu} et al., J. Symb. Comput. 55, 72--95 (2013; Zbl 1325.68292) Full Text: DOI
Liu, Yinping; Liao, Shijun; Li, Zhibin A Maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations. (English) Zbl 1255.93054 J. Syst. Sci. Complex. 25, No. 3, 594-616 (2012). MSC: 93B40 93C15 PDFBibTeX XMLCite \textit{Y. Liu} et al., J. Syst. Sci. Complex. 25, No. 3, 594--616 (2012; Zbl 1255.93054) Full Text: DOI
Zhao, Yinlong; Lin, Zhiliang; Liu, Zeng; Liao, Shijun The improved homotopy analysis method for the Thomas-Fermi equation. (English) Zbl 1245.65099 Appl. Math. Comput. 218, No. 17, 8363-8369 (2012). MSC: 65L10 PDFBibTeX XMLCite \textit{Y. Zhao} et al., Appl. Math. Comput. 218, No. 17, 8363--8369 (2012; Zbl 1245.65099) Full Text: DOI
Lin, Zhiliang; Liao, Shijun The scaled boundary FEM for nonlinear problems. (English) Zbl 1221.65305 Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 63-75 (2011). MSC: 65N30 65N99 PDFBibTeX XMLCite \textit{Z. Lin} and \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 63--75 (2011; Zbl 1221.65305) Full Text: DOI
Kousar, Nabeela; Liao, Shijun Unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet. (English) Zbl 1206.35208 Nonlinear Anal., Real World Appl. 12, No. 1, 333-342 (2011). MSC: 35Q35 35C20 76D10 35B30 PDFBibTeX XMLCite \textit{N. Kousar} and \textit{S. Liao}, Nonlinear Anal., Real World Appl. 12, No. 1, 333--342 (2011; Zbl 1206.35208) Full Text: DOI
Li, Yajie; Nohara, Ben T.; Liao, Shijun Series solutions of coupled Van der Pol equation by means of homotopy analysis method. (English) Zbl 1311.70031 J. Math. Phys. 51, No. 6, 063517, 12 p. (2010). MSC: 70K30 70K40 34C15 65H20 34C25 78A55 37N05 PDFBibTeX XMLCite \textit{Y. Li} et al., J. Math. Phys. 51, No. 6, 063517, 12 p. (2010; Zbl 1311.70031) Full Text: DOI Link
Liu, Zeng; Oberlack, Martin; Grebenev, Vladimir N.; Liao, Shi-Jun Explicit series solution of a closure model for the von Kármán-Howarth equation. (English) Zbl 1235.34065 ANZIAM J. 52, No. 2, 179-202 (2010). Reviewer: Zhanbing Bai (Qingdao) MSC: 34B15 34A05 34A45 34A25 PDFBibTeX XMLCite \textit{Z. Liu} et al., ANZIAM J. 52, No. 2, 179--202 (2010; Zbl 1235.34065) Full Text: DOI
Liao, Shijun An optimal homotopy-analysis approach for strongly nonlinear differential equations. (English) Zbl 1222.65088 Commun. Nonlinear Sci. Numer. Simul. 15, No. 8, 2003-2016 (2010). MSC: 65L99 34A25 34A45 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 8, 2003--2016 (2010; Zbl 1222.65088) Full Text: DOI
Liao, Shijun On the relationship between the homotopy analysis method and Euler transform. (English) Zbl 1221.65206 Commun. Nonlinear Sci. Numer. Simul. 15, No. 6, 1421-1431 (2010). MSC: 65L99 34E10 34A45 41A58 40G05 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 6, 1421--1431 (2010; Zbl 1221.65206) Full Text: DOI
Cheng, Jun; Zhu, Song-Ping; Liao, Shi-Jun An explicit series approximation to the optimal exercise boundary of American put options. (English) Zbl 1221.91053 Commun. Nonlinear Sci. Numer. Simul. 15, No. 5, 1148-1158 (2010). MSC: 91G60 65M99 91G20 PDFBibTeX XMLCite \textit{J. Cheng} et al., Commun. Nonlinear Sci. Numer. Simul. 15, No. 5, 1148--1158 (2010; Zbl 1221.91053) Full Text: DOI
Khan, Hina; Liao, Shi-Jun; Mohapatra, R. N.; Vajravelu, K. An analytical solution for a nonlinear time-delay model in biology. (English) Zbl 1221.65204 Commun. Nonlinear Sci. Numer. Simul. 14, No. 7, 3141-3148 (2009). MSC: 65L99 37N25 PDFBibTeX XMLCite \textit{H. Khan} et al., Commun. Nonlinear Sci. Numer. Simul. 14, No. 7, 3141--3148 (2009; Zbl 1221.65204) Full Text: DOI
Liao, Shi-Jun A general approach to get series solution of non-similarity boundary-layer flows. (English) Zbl 1221.76068 Commun. Nonlinear Sci. Numer. Simul. 14, No. 5, 2144-2159 (2009). MSC: 76D10 PDFBibTeX XMLCite \textit{S.-J. Liao}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 5, 2144--2159 (2009; Zbl 1221.76068) Full Text: DOI
Liao, Shijun Notes on the homotopy analysis method: some definitions and theorems. (English) Zbl 1221.65126 Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 983-997 (2009). MSC: 65H99 35A25 35C10 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 983--997 (2009; Zbl 1221.65126) Full Text: DOI
Khan, Hina; Mohapatra, Ram N.; Vajravelu, K.; Liao, S. J. The explicit series solution of SIR and SIS epidemic models. (English) Zbl 1171.92033 Appl. Math. Comput. 215, No. 2, 653-669 (2009). MSC: 92D30 37N25 34A34 PDFBibTeX XMLCite \textit{H. Khan} et al., Appl. Math. Comput. 215, No. 2, 653--669 (2009; Zbl 1171.92033) Full Text: DOI
Cheng, Jun; Cang, Jie; Liao, Shijun On the interaction of deep water waves and exponential shear currents. (English) Zbl 1173.76007 Z. Angew. Math. Phys. 60, No. 3, 450-478 (2009). MSC: 76B15 76M25 PDFBibTeX XMLCite \textit{J. Cheng} et al., Z. Angew. Math. Phys. 60, No. 3, 450--478 (2009; Zbl 1173.76007) Full Text: DOI
Abbasbandy, Saeid; Liao, Shi-Jun A new modification of false position method based on homotopy analysis method. (English) Zbl 1231.65084 Appl. Math. Mech., Engl. Ed. 29, No. 2, 223-228 (2008). MSC: 65H05 65H20 PDFBibTeX XMLCite \textit{S. Abbasbandy} and \textit{S.-J. Liao}, Appl. Math. Mech., Engl. Ed. 29, No. 2, 223--228 (2008; Zbl 1231.65084) Full Text: DOI
Wang, Ji; Chen, Jiankang; Liao, Shijun An explicit solution of the large deformation of a cantilever beam under point load at the free tip. (English) Zbl 1128.74026 J. Comput. Appl. Math. 212, No. 2, 320-330 (2008). MSC: 74K10 74G05 PDFBibTeX XMLCite \textit{J. Wang} et al., J. Comput. Appl. Math. 212, No. 2, 320--330 (2008; Zbl 1128.74026) Full Text: DOI
Xu, Hang; Liao, Shi-Jun Dual solutions of boundary layer flow over an upstream moving plate. (English) Zbl 1131.35066 Commun. Nonlinear Sci. Numer. Simul. 13, No. 2, 350-358 (2008). MSC: 35Q35 76D10 PDFBibTeX XMLCite \textit{H. Xu} and \textit{S.-J. Liao}, Commun. Nonlinear Sci. Numer. Simul. 13, No. 2, 350--358 (2008; Zbl 1131.35066) Full Text: DOI
Liao, Shi-Jun A new branch of solutions of boundary-layer flows over a permeable stretching plate. (English) Zbl 1200.76046 Int. J. Non-Linear Mech. 42, No. 6, 819-830 (2007). MSC: 76D10 PDFBibTeX XMLCite \textit{S.-J. Liao}, Int. J. Non-Linear Mech. 42, No. 6, 819--830 (2007; Zbl 1200.76046) Full Text: DOI
Tan, Yue; Xu, Hang; Liao, Shi-Jun Explicit series solution of travelling waves with a front of Fisher equation. (English) Zbl 1143.35313 Chaos Solitons Fractals 31, No. 2, 462-472 (2007). MSC: 35C10 35K57 PDFBibTeX XMLCite \textit{Y. Tan} et al., Chaos Solitons Fractals 31, No. 2, 462--472 (2007; Zbl 1143.35313) Full Text: DOI
Abbasbandy, S.; Tan, Y.; Liao, S. J. Newton-homotopy analysis method for nonlinear equations. (English) Zbl 1119.65032 Appl. Math. Comput. 188, No. 2, 1794-1800 (2007). MSC: 65H05 65H20 PDFBibTeX XMLCite \textit{S. Abbasbandy} et al., Appl. Math. Comput. 188, No. 2, 1794--1800 (2007; Zbl 1119.65032) Full Text: DOI
Xu, Hang; Liao, Shijun; Pop, Ioan Series solutions of unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. (English) Zbl 1105.76061 Eur. J. Mech., B, Fluids 26, No. 1, 15-27 (2007). MSC: 76W05 76D10 76M45 80A20 PDFBibTeX XMLCite \textit{H. Xu} et al., Eur. J. Mech., B, Fluids 26, No. 1, 15--27 (2007; Zbl 1105.76061) Full Text: DOI
Xu, Hang; Liao, Shi-Jun Series solutions of unsteady MHD flows above a rotating disk. (English) Zbl 1163.76452 Meccanica 41, No. 6, 599-609 (2006). MSC: 76W05 76U05 PDFBibTeX XMLCite \textit{H. Xu} and \textit{S.-J. Liao}, Meccanica 41, No. 6, 599--609 (2006; Zbl 1163.76452) Full Text: DOI
Xu, H.; Liao, S. J.; Pop, I. Series solutions of unsteady boundary-layer flow of a micropolar fluid near the forward stagnation point of a plane surface. (English) Zbl 1096.76004 Acta Mech. 184, No. 1-4, 87-101 (2006). MSC: 76A05 76M45 PDFBibTeX XMLCite \textit{H. Xu} et al., Acta Mech. 184, No. 1--4, 87--101 (2006; Zbl 1096.76004) Full Text: DOI
Yang, Cheng; Liao, Shijun On the explicit, purely analytic solution of von Kármán swirling viscous flow. (English) Zbl 1075.35059 Commun. Nonlinear Sci. Numer. Simul. 11, No. 1, 83-93 (2006). MSC: 35Q35 76D17 35C05 76U05 PDFBibTeX XMLCite \textit{C. Yang} and \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 11, No. 1, 83--93 (2006; Zbl 1075.35059) Full Text: DOI
Liao, Shijun A new branch of solutions of boundary-layer flows over an impermeable stretched plate. (English) Zbl 1189.76142 Int. J. Heat Mass Transfer 48, No. 12, 2529-2539 (2005). MSC: 76D10 76M55 PDFBibTeX XMLCite \textit{S. Liao}, Int. J. Heat Mass Transfer 48, No. 12, 2529--2539 (2005; Zbl 1189.76142) Full Text: DOI
Liao, Shijun Comparison between the homotopy analysis method and homotopy perturbation method. (English) Zbl 1082.65534 Appl. Math. Comput. 169, No. 2, 1186-1194 (2005). MSC: 65H20 PDFBibTeX XMLCite \textit{S. Liao}, Appl. Math. Comput. 169, No. 2, 1186--1194 (2005; Zbl 1082.65534) Full Text: DOI
Li, Shuicai; Liao, Shi-Jun An analytic approach to solve multiple solutions of a strongly nonlinear problem. (English) Zbl 1151.35354 Appl. Math. Comput. 169, No. 2, 854-865 (2005). MSC: 35J60 34B15 PDFBibTeX XMLCite \textit{S. Li} and \textit{S.-J. Liao}, Appl. Math. Comput. 169, No. 2, 854--865 (2005; Zbl 1151.35354) Full Text: DOI
Wu, Y. Y.; Liao, S. J.; Zhao, X. Y. Some notes on the general boundary element method for highly nonlinear problems. (English) Zbl 1147.76596 Commun. Nonlinear Sci. Numer. Simul. 10, No. 7, 725-735 (2005). MSC: 76M15 80M15 80A20 PDFBibTeX XMLCite \textit{Y. Y. Wu} et al., Commun. Nonlinear Sci. Numer. Simul. 10, No. 7, 725--735 (2005; Zbl 1147.76596) Full Text: DOI
Liao, Shijun; Pop, Ioan Explicit analytic solution for similarity boundary layer equations. (English) Zbl 1045.76008 Int. J. Heat Mass Transfer 47, No. 1, 75-85 (2004). MSC: 76D10 76M55 76S05 PDFBibTeX XMLCite \textit{S. Liao} and \textit{I. Pop}, Int. J. Heat Mass Transfer 47, No. 1, 75--85 (2004; Zbl 1045.76008) Full Text: DOI
Liao, Shijun On the homotopy analysis method for nonlinear problems. (English) Zbl 1086.35005 Appl. Math. Comput. 147, No. 2, 499-513 (2004). MSC: 35A25 76M25 76D10 PDFBibTeX XMLCite \textit{S. Liao}, Appl. Math. Comput. 147, No. 2, 499--513 (2004; Zbl 1086.35005) Full Text: DOI
Wang, C.; Liao, S. J.; Zhu, J. M. An explicit analytic solution for non-Darcy natural convection over horizontal plate with surface mass flux and thermal dispersion effects. (English) Zbl 1064.76103 Acta Mech. 165, No. 3-4, 139-150 (2003). MSC: 76R10 76S05 80A20 PDFBibTeX XMLCite \textit{C. Wang} et al., Acta Mech. 165, No. 3--4, 139--150 (2003; Zbl 1064.76103) Full Text: DOI
Wang, Chun; Liao, Shijun; Zhu, Jimao An explicit solution for the combined heat and mass transfer by natural convection from a vertical wall in a non-Darcy porous medium. (English) Zbl 1046.76047 Int. J. Heat Mass Transfer 46, No. 25, 4813-4822 (2003). MSC: 76R10 76S05 80A20 PDFBibTeX XMLCite \textit{C. Wang} et al., Int. J. Heat Mass Transfer 46, No. 25, 4813--4822 (2003; Zbl 1046.76047) Full Text: DOI
Liao, Shijun On a generalized Taylor theorem: a rational proof of the validity of the homotopy analysis method. (English) Zbl 1044.41019 Appl. Math. Mech., Engl. Ed. 24, No. 1, 53-60 (2003). Reviewer: László Leindler (Szeged) MSC: 41A58 26A06 PDFBibTeX XMLCite \textit{S. Liao}, Appl. Math. Mech., Engl. Ed. 24, No. 1, 53--60 (2003; Zbl 1044.41019) Full Text: DOI
Wang, C.; Zhu, J. M.; Liao, S. J.; Pop, I. On the explicit analytic solution of Cheng-Chang equation. (English) Zbl 1029.76050 Int. J. Heat Mass Transfer 46, No. 10, 1855-1860 (2003). MSC: 76R10 76S05 80A20 PDFBibTeX XMLCite \textit{C. Wang} et al., Int. J. Heat Mass Transfer 46, No. 10, 1855--1860 (2003; Zbl 1029.76050) Full Text: DOI
Liao, Shi-Jun; Cheung, Kwok Fai Homotopy analysis of nonlinear progressive waves in deep water. (English) Zbl 1112.76316 J. Eng. Math. 45, No. 2, 105-116 (2003). MSC: 76B15 76M25 PDFBibTeX XMLCite \textit{S.-J. Liao} and \textit{K. F. Cheung}, J. Eng. Math. 45, No. 2, 105--116 (2003; Zbl 1112.76316) Full Text: DOI
Liao, Shi-Jun An analytic approximation of the drag coefficient for the viscous flow past a sphere. (English) Zbl 1116.76335 Int. J. Non-Linear Mech. 37, No. 1, 1-18 (2002). MSC: 76D05 35Q30 76M25 PDFBibTeX XMLCite \textit{S.-J. Liao}, Int. J. Non-Linear Mech. 37, No. 1, 1--18 (2002; Zbl 1116.76335) Full Text: DOI
Liao, Shijun; Campo, Antonio Analytic solutions of the temperature distribution in Blasius viscous flow problems. (English) Zbl 1007.76014 J. Fluid Mech. 453, 411-425 (2002). MSC: 76D10 76M25 80A20 68W30 PDFBibTeX XMLCite \textit{S. Liao} and \textit{A. Campo}, J. Fluid Mech. 453, 411--425 (2002; Zbl 1007.76014) Full Text: DOI
Liao, Shijun; Mashayek, F. A multigrid approach for steady-state laminar viscous flows. (English) Zbl 1002.76091 Int. J. Numer. Methods Fluids 37, No. 1, 107-123 (2001). MSC: 76M25 76D05 65N55 PDFBibTeX XMLCite \textit{S. Liao} and \textit{F. Mashayek}, Int. J. Numer. Methods Fluids 37, No. 1, 107--123 (2001; Zbl 1002.76091) Full Text: DOI
Liao, Shijun A non-iterative numerical approach for two-dimensional viscous flow problems governed by the Falkner-Skan equation. (English) Zbl 0990.76068 Int. J. Numer. Methods Fluids 35, No. 5, 495-518 (2001). MSC: 76M25 76D10 PDFBibTeX XMLCite \textit{S. Liao}, Int. J. Numer. Methods Fluids 35, No. 5, 495--518 (2001; Zbl 0990.76068) Full Text: DOI
Liao, Shi-Jun An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. (English) Zbl 1342.74180 Int. J. Non-Linear Mech. 34, No. 4, 759-778 (1999). MSC: 74S30 34A05 PDFBibTeX XMLCite \textit{S.-J. Liao}, Int. J. Non-Linear Mech. 34, No. 4, 759--778 (1999; Zbl 1342.74180) Full Text: DOI
Liao, Shijun A simple approach of enlarging convergence regions of perturbation approximations. (English) Zbl 0949.70003 Nonlinear Dyn. 19, No. 2, 93-110 (1999). MSC: 70-08 70K60 34A25 65B10 PDFBibTeX XMLCite \textit{S. Liao}, Nonlinear Dyn. 19, No. 2, 93--110 (1999; Zbl 0949.70003) Full Text: DOI
Liao, Shijun The general boundary element method and its further generalizations. (English) Zbl 0954.76060 Int. J. Numer. Methods Fluids 31, No. 3, 627-655 (1999). MSC: 76M15 65N38 PDFBibTeX XMLCite \textit{S. Liao}, Int. J. Numer. Methods Fluids 31, No. 3, 627--655 (1999; Zbl 0954.76060) Full Text: DOI
Liao, Shijun A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate. (English) Zbl 0931.76017 J. Fluid Mech. 385, 101-128 (1999). MSC: 76D10 76M45 PDFBibTeX XMLCite \textit{S. Liao}, J. Fluid Mech. 385, 101--128 (1999; Zbl 0931.76017) Full Text: DOI
Liao, Shijun On the general boundary element method. (English) Zbl 0940.65141 Eng. Anal. Bound. Elem. 21, No. 1, 39-51 (1998). Reviewer: C.I.Gheorghiu (Cluj-Napoca) MSC: 65N38 35J65 PDFBibTeX XMLCite \textit{S. Liao}, Eng. Anal. Bound. Elem. 21, No. 1, 39--51 (1998; Zbl 0940.65141) Full Text: DOI
Liao, Shijun General boundary element method: An application of homotopy analysis method. (English) Zbl 0918.65074 Commun. Nonlinear Sci. Numer. Simul. 3, No. 3, 159-163 (1998). MSC: 65N38 35J65 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 3, No. 3, 159--163 (1998; Zbl 0918.65074) Full Text: DOI
Liao, Shijun On the 8th-order drag coefficient formula of a sphere in a uniform stream: A simplified description. (English) Zbl 0924.35109 Commun. Nonlinear Sci. Numer. Simul. 3, No. 4, 256-260 (1998). MSC: 35Q35 76D05 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 3, No. 4, 256--260 (1998; Zbl 0924.35109) Full Text: DOI
Liao, Shi-Jun An explicit, totally analytic solution of laminar viscous flow over a semi-infinite flat plate. (English) Zbl 0922.34012 Commun. Nonlinear Sci. Numer. Simul. 3, No. 2, 53-57 (1998). MSC: 34B05 76M35 76D33 35Q35 34A05 PDFBibTeX XMLCite \textit{S.-J. Liao}, Commun. Nonlinear Sci. Numer. Simul. 3, No. 2, 53--57 (1998; Zbl 0922.34012) Full Text: DOI
Liao, Shijun Numerically solving strongly nonlinear problems by means of no iterations. (English) Zbl 0916.76057 J. Hydrodyn., Ser. B 10, No. 1, 102-108 (1998). MSC: 76M25 76D10 PDFBibTeX XMLCite \textit{S. Liao}, J. Hydrodyn., Ser. B 10, No. 1, 102--108 (1998; Zbl 0916.76057)
Liao, Shijun Homotopy analysis method: A new analytical technique for nonlinear problems. (English) Zbl 0927.65069 Commun. Nonlinear Sci. Numer. Simul. 2, No. 2, electronic paper No. 8 (1997). MSC: 65H20 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 2, No. 2, electronic paper No. 8 (1997; Zbl 0927.65069) Full Text: DOI
Liao, Shijun; Zhu, Jimao A short note on high-order streamfunction-vorticity formulations of 2D steady state Navier-Stokes equations. (English) Zbl 0873.76052 Int. J. Numer. Methods Fluids 22, No. 1, 1-9 (1996). MSC: 76M20 76D05 PDFBibTeX XMLCite \textit{S. Liao} and \textit{J. Zhu}, Int. J. Numer. Methods Fluids 22, No. 1, 1--9 (1996; Zbl 0873.76052) Full Text: DOI
Liao, S. J.; Chwang, Allen T. General boundary element method for nonlinear problems. (English) Zbl 0863.76037 Int. J. Numer. Methods Fluids 23, No. 5, 467-483 (1996). MSC: 76M15 76D10 PDFBibTeX XMLCite \textit{S. J. Liao} and \textit{A. T. Chwang}, Int. J. Numer. Methods Fluids 23, No. 5, 467--483 (1996; Zbl 0863.76037) Full Text: DOI
Liao, Shijun What’s the common ground of all numerical and analytical techniques for nonlinear problems? (English) Zbl 0924.65047 Commun. Nonlinear Sci. Numer. Simul. 1, No. 4, electronic paper No. 6 (1996). MSC: 65J05 47J25 65H20 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 1, No. 4, electronic paper No. 6 (1996; Zbl 0924.65047) Full Text: DOI
Liao, Shijun High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators. (English) Zbl 0882.65108 Int. J. Numer. Methods Fluids 23, No. 8, 739-751 (1996). Reviewer: C.I.Gheorghiu (Cluj-Napoca) MSC: 65N38 35J65 PDFBibTeX XMLCite \textit{S. Liao}, Int. J. Numer. Methods Fluids 23, No. 8, 739--751 (1996; Zbl 0882.65108) Full Text: DOI
Liao, Shijun An approximate solution technique not depending on small parameters: A special example. (English) Zbl 0837.76073 Int. J. Non-Linear Mech. 30, No. 3, 371-380 (1995). MSC: 76M99 34A45 PDFBibTeX XMLCite \textit{S. Liao}, Int. J. Non-Linear Mech. 30, No. 3, 371--380 (1995; Zbl 0837.76073) Full Text: DOI
Liao, S. J. Higher-order streamfunction-vorticity formulation of 2D steady-state Navier-Stokes equations. (English) Zbl 0762.76063 Int. J. Numer. Methods Fluids 15, No. 5, 595-612 (1992). MSC: 76M15 76D05 PDFBibTeX XMLCite \textit{S. J. Liao}, Int. J. Numer. Methods Fluids 15, No. 5, 595--612 (1992; Zbl 0762.76063) Full Text: DOI