A new analytic algorithm of Lane-Emden type equations. - Shijun Liao (Appl. Math. Comput., 2003)

An explicit analytic solution to the Thomas-Fermi equation. - Shijun Liao (Appl. Math. Comput., 2003)

On the homotopy analysis method for nonlinear problems. - Shijun Liao (Appl. Math. Comput., 2004)

An analytic approach to solve multiple solutions of a strongly nonlinear problem. - Shuicai Li; Shijun Liao (Appl. Math. Comput., 2005)

Comparison between the homotopy analysis method and homotopy perturbation method. - Shijun Liao (Appl. Math. Comput., 2005)

Newton-homotopy analysis method for nonlinear equations. - Saeid Abbasbandy; Y. Tan; Shijun Liao (Appl. Math. Comput., 2007)

The explicit series solution of SIR and SIS epidemic models. - Hina Khan; Ram N. Mohapatra; K. Vajravelu; Shijun Liao (Appl. Math. Comput., 2009)

Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet. - Hang Xu 005; Shijun Liao (Comput. Math. Appl., 2009)

The improved homotopy analysis method for the Thomas-Fermi equation. - Yinlong Zhao; Zhiliang Lin; Zeng Liu; Shijun Liao (Appl. Math. Comput., 2012)

A maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations. - Yinping Liu; Shijun Liao; Zhibin Li 005 (J. Syst. Sci. Complex., 2012)

An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain. - Yinlong Zhao; Zhiliang Lin; Shijun Liao (Comput. Phys. Commun., 2013)

Symbolic computation of strongly nonlinear periodic oscillations. - Yinping Liu; Shijun Liao; Zhibin Li 005 (J. Symb. Comput., 2013)

Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. - Umer Farooq; Tasawar Hayat; Ahmed Alsaedi; Shijun Liao (Appl. Math. Comput., 2014)

Physical limit of prediction for chaotic motion of three-body problem. - Shijun Liao (Commun. Nonlinear Sci. Numer. Simul., 2014)

Do peaked solitary water waves indeed exist? - Shijun Liao (Commun. Nonlinear Sci. Numer. Simul., 2014)

Can We Obtain a Reliable Convergent Chaotic Solution in any Given Finite Interval of Time? - Shijun Liao (Int. J. Bifurc. Chaos, 2014)

On cusped solitary waves in finite water depth. - Shijun Liao (Commun. Nonlinear Sci. Numer. Simul., 2015)

On the Inherent Self-Excited Macroscopic Randomness of Chaotic Three-Body Systems. - Shijun Liao; Xiaoming Li (Int. J. Bifurc. Chaos, 2015)

Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces. - Umer Farooq; Tasawar Hayat; Ahmed Alsaedi; Shijun Liao (Numer. Algorithms, 2015)

A HAM-based analytic approach for physical models with an infinite number of singularities. - Dali Xu; Jifeng Cui; Shijun Liao; Ahmed Alsaedi (Numer. Algorithms, 2015)

On the method of directly defining inverse mapping for nonlinear differential equations. - Shijun Liao; Yinlong Zhao (Numer. Algorithms, 2016)

A HAM-based wavelet approach for nonlinear ordinary differential equations. - Zhaochen Yang; Shijun Liao (Commun. Nonlinear Sci. Numer. Simul., 2017)

A HAM-based wavelet approach for nonlinear partial differential equations: Two dimensional Bratu problem as an application. - Zhaochen Yang; Shijun Liao (Commun. Nonlinear Sci. Numer. Simul., 2017)

On the homotopy analysis method for backward/forward-backward stochastic differential equations. - Xiaoxu Zhong; Shijun Liao (Numer. Algorithms, 2017)

On the generalized wavelet-Galerkin method. - Zhaochen Yang; Shijun Liao (J. Comput. Appl. Math., 2018)

Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach. - Qiang Yu; Hang Xu 005; Shijun Liao (Numer. Algorithms, 2018)

A novel homotopy-wavelet approach for solving stream function-vorticity formulation of Navier-Stokes equations. - Qiang Yu; Hang Xu 005; Shijun Liao; Zhaochen Yang (Commun. Nonlinear Sci. Numer. Simul., 2019)

High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow. - Bin Xie; Xi Deng; Shijun Liao; Feng Xiao 001 (J. Comput. Phys., 2019)

On the risks of using double precision in numerical simulations of spatio-temporal chaos. - Tianli Hu; Shijun Liao (J. Comput. Phys., 2020)

A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids. - Bin Xie; Peng Jin; Hiroki Nakayama; Shijun Liao; Feng Xiao 001 (J. Comput. Phys., 2020)

Three-body problem - from Newton to supercomputer plus machine learning. - Shijun Liao; Xiaoming Li; Yu Yang (CoRR, 2021)

On Reliable Computation of Lifetime in Transient Chaos. - Tianzhuang Xu; Bin Xie; Shijun Liao (Int. J. Bifurc. Chaos, 2021)

Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method. - Bin Xie; Xi Deng; Shijun Liao; Feng Xiao 001 (J. Comput. Phys., 2021)

Ultra-Chaos in the Motion of Walking Droplet. - Yu Yang; Shijie Qin; Shijun Liao (Int. J. Bifurc. Chaos, 2023)

Noise-expansion cascade: an origin of randomness of turbulence. - Shijun Liao; Shijie Qin (CoRR, 2024)

Ultra-Chaos: A Great Challenge for Machine Learning and AI. - Yu Yang; Shijun Liao (Int. J. Bifurc. Chaos, 2024)

An automated parallel program of Clean Numerical Simulation for chaotic systems governed by ODEs. - Bo Zhang; Shijun Liao (Comput. Phys. Commun., 2025)

Physical significance of artificial numerical noise in direct numerical simulation of turbulence. - Shijun Liao; Shijie Qin (CoRR, 2025)

Clean numerical simulation (CNS) of three-dimensional turbulent Kolmogorov flow. - Shijie Qin; Shijun Liao (CoRR, 2025)

An accurate THINC scheme for interface capturing based on homotopy analysis method. - Dezhu Chen; Shijun Liao; Bin Xie (J. Comput. Phys., 2026)