Unconditional Stability of Corrected Explicit-Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations. - Han-Sheng Shi; Hong-Lin Liao (SIAM J. Numer. Anal., 2006)

Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations. - Hong-Lin Liao; Zhi-Zhong Sun; Han-Sheng Shi (SIAM J. Numer. Anal., 2010)

Maximum norm error estimates of efficient difference schemes for second-order wave equations. - Hong-Lin Liao; Zhi-Zhong Sun (J. Comput. Appl. Math., 2011)

A two-level compact ADI method for solving second-order wave equations. - Hong-Lin Liao; Zhi-Zhong Sun (Int. J. Comput. Math., 2013)

Linearly localized difference schemes for the nonlinear Maxwell model of a magnetic field into a substance. - Hong-Lin Liao; Ying Zhao (Appl. Math. Comput., 2014)

Numerical study of fourth-order linearized compact schemes for generalized NLS equations. - Hong-Lin Liao; Han-Sheng Shi; Ying Zhao (Comput. Phys. Commun., 2014)

Finite difference methods for the time fractional diffusion equation on non-uniform meshes. - Ya-nan Zhang 003; Zhi-Zhong Sun; Hong-Lin Liao (J. Comput. Phys., 2014)

Stability and Convergence of Modified Du Fort-Frankel Schemes for Solving Time-Fractional Subdiffusion Equations. - Hong-Lin Liao; Ya-nan Zhang 003; Ying Zhao; Han-Sheng Shi (J. Sci. Comput., 2014)

A center Box method for radially symmetric solution of fractional subdiffusion equation. - Xiuling Hu; Hong-Lin Liao; Fawang Liu; Ian W. Turner (Appl. Math. Comput., 2015)

A Weighted ADI Scheme for Subdiffusion Equations. - Hong-Lin Liao; Ying Zhao; Xing-hu Teng (J. Sci. Comput., 2016)

Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations. - Hong-Lin Liao; Pin Lyu; Seakweng Vong; Ying Zhao (Numer. Algorithms, 2017)

Second-order BDF time approximation for Riesz space-fractional diffusion equations. - Hong-Lin Liao; Pin Lyu; Seakweng Vong (Int. J. Comput. Math., 2018)

Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations. - Hong-Lin Liao; Dongfang Li; Jiwei Zhang 002 (SIAM J. Numer. Anal., 2018)

A fourth-order compact solver for fractional-in-time fourth-order diffusion equations. - Jialing Zhong; Hong-lin Liao; Bingquan Ji; Luming Zhang (CoRR, 2019)

Unconditional Convergence of a Fast Two-Level Linearized Algorithm for Semilinear Subdiffusion Equations. - Hong-lin Liao; Yonggui Yan; Jiwei Zhang 002 (J. Sci. Comput., 2019)

A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems. - Hong-lin Liao; William McLean; Jiwei Zhang 002 (SIAM J. Numer. Anal., 2019)

Simple maximum principle preserving time-stepping methods for time-fractional Allen-Cahn equation. - Bingquan Ji; Hong-lin Liao; Luming Zhang (Adv. Comput. Math., 2020)

Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint. - Bingquan Ji; Hong-lin Liao; Yuezheng Gong; Luming Zhang (Commun. Nonlinear Sci. Numer. Simul., 2020)

An adaptive BDF2 implicit time-stepping method for the phase field crystal model. - Hong-lin Liao; Bingquan Ji; Luming Zhang (CoRR, 2020)

Analysis of the second order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection. - Hong-lin Liao; Xuehua Song; Tao Tang 003; Tao Zhou 010 (CoRR, 2020)

Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (CoRR, 2020)

A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (J. Comput. Phys., 2020)

Superconvergence Error Estimate of a Finite Element Method on Nonuniform Time Meshes for Reaction-Subdiffusion Equations. - Jincheng Ren; Hong-lin Liao; Zhimin Zhang 002 (J. Sci. Comput., 2020)

Sharp H1-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations. - Xin Li 075; Luming Zhang; Hong-lin Liao (Numer. Algorithms, 2020)

On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen-Cahn Equation. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (SIAM J. Numer. Anal., 2020)

Adaptive Second-Order Crank-Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models. - Bingquan Ji; Hong-lin Liao; Yuezheng Gong; Luming Zhang (SIAM J. Sci. Comput., 2020)

Mesh-robustness of the variable steps BDF2 method for the Cahn-Hilliard model. - Hong-lin Liao; Bingquan Ji; Lin Wang; Zhimin Zhang 002 (CoRR, 2021)

A new discrete energy technique for multi-step backward difference formulas. - Hong-Lin Liao; Tao Tang 003; Tao Zhou 010 (CoRR, 2021)

The variable-step L1 scheme preserving a compatible energy law for time-fractional Allen-Cahn equation. - Hong-lin Liao; Xiaohan Zhu; Jindi Wang (CoRR, 2021)

Sharp H1-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems. - Jincheng Ren; Hong-lin Liao; Jiwei Zhang 002; Zhimin Zhang 002 (J. Comput. Appl. Math., 2021)

Analysis of adaptive BDF2 scheme for diffusion equations. - Hong-lin Liao; Zhimin Zhang 002 (Math. Comput., 2021)

A second-order fast compact scheme with unequal time-steps for subdiffusion problems. - Xin Li 075; Hong-lin Liao; Luming Zhang (Numer. Algorithms, 2021)

An Energy Stable and Maximum Bound Preserving Scheme with Variable Time Steps for Time Fractional Allen-Cahn Equation. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (SIAM J. Sci. Comput., 2021)

Asymptotically compatible energy law of the Crank-Nicolson type schemes for time-fractional MBE models. - Xiaohan Zhu; Hong-lin Liao (Appl. Math. Lett., 2022)

Discrete gradient structures of BDF methods up to fifth-order for the phase field crystal model. - Hong-lin Liao; Yuanyuan Kang; Wenzhe Han (CoRR, 2022)

Energy stability of variable-step L1-type schemes for time-fractional Cahn-Hilliard model. - Bingquan Ji; Xiaohan Zhu; Hong-lin Liao (CoRR, 2022)

Discrete energy analysis of the third-order variable-step BDF time-stepping for diffusion equations. - Hong-lin Liao; Tao Tang 003; Tao Zhou 010 (CoRR, 2022)

Compatible L2 norm convergence of variable-step L1 scheme for the time-fractional MBE mobel with slope selection. - Yin Yang 003; Jindi Wang; Yanping Chen 002; Hong-lin Liao (CoRR, 2022)

Asymptotically compatible energy of variable-step fractional BDF2 formula for time-fractional Cahn-Hilliard model. - Hong-lin Liao; Nan Liu; Xuan Zhao 004 (CoRR, 2022)

Compatible L2 norm convergence of variable-step L1 scheme for the time-fractional MBE model with slope selection. - Yin Yang 003; Jindi Wang; Yanping Chen 002; Hong-lin Liao (J. Comput. Phys., 2022)

Energy Stability of BDF Methods up to Fifth-Order for the Molecular Beam Epitaxial Model Without Slope Selection. - Yuanyuan Kang; Hong-lin Liao (J. Sci. Comput., 2022)

Mesh-Robustness of an Energy Stable BDF2 Scheme with Variable Steps for the Cahn-Hilliard Model. - Hong-lin Liao; Bingquan Ji; Lin Wang; Zhimin Zhang 002 (J. Sci. Comput., 2022)

Stability of Variable-Step BDF2 and BDF3 Methods. - Zhaoyi Li; Hong-lin Liao (SIAM J. Numer. Anal., 2022)

An energy stable linear BDF2 scheme with variable time-steps for the molecular beam epitaxial model without slope selection. - Yuanyuan Kang; Hong-lin Liao; Jindi Wang (Commun. Nonlinear Sci. Numer. Simul., 2023)

Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models. - Hong-lin Liao; Nan Liu; Pin Lyu (SIAM J. Numer. Anal., 2023)

Energy dissipation laws of time filtered BDF methods up to fourth-order for the molecular beam epitaxial equation. - Jiexin Wang; Yuanyuan Kang; Hong-lin Liao (Commun. Nonlinear Sci. Numer. Simul., 2024)

Mesh-robust stability and convergence of variable-step deferred correction methods based on the BDF2 formula. - Jiahe Yue; Hong-lin Liao; Nan Liu (CoRR, 2024)

Average energy dissipation rates of additive implicit-explicit Runge-Kutta methods for gradient flow problems. - Hong-lin Liao; Xuping Wang; Cao Wen (CoRR, 2024)

A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model. - Hong-lin Liao; Tao Tang 003; Xuping Wang; Tao Zhou 010 (CoRR, 2024)

Original energy dissipation preserving corrections of integrating factor Runge-Kutta methods for gradient flow problems. - Hong-lin Liao; Xuping Wang; Cao Wen (J. Comput. Phys., 2024)

High-order energy stable variable-step schemes for the time-fractional Cahn-Hilliard model. - Haiqing Zhang; Hong-lin Liao (Math. Comput. Simul., 2024)

Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems. - Hong-lin Liao; Xuping Wang (Math. Comput., 2024)

Asymptotically Compatible Energy and Dissipation Law of the Nonuniform L2-1σ Scheme for Time Fractional Allen-Cahn Model. - Hong-lin Liao; Xiaohan Zhu; Hong Sun (J. Sci. Comput., 2024)

A Unified L2 Norm Error Analysis of SAV-BDF Schemes for the Incompressible Navier-Stokes Equations. - Bingquan Ji; Hong-lin Liao (J. Sci. Comput., 2024)

A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint. - Xu Liu; Qi Hong; Hong-lin Liao; Yuezheng Gong (Numer. Algorithms, 2024)

A Unified Framework on the Original Energy Laws of Three Effective Classes of Runge-Kutta Methods for Phase Field Crystal Type Models. - Xuping Wang; Xuan Zhao 004; Hong-lin Liao (SIAM J. Numer. Anal., 2025)

Mesh-Robust Convergence of a Third-Order Variable-Step Deferred Correction Method for the Cahn-Hilliard Model. - Nan Liu; Jiahe Yue; Hong-lin Liao (J. Sci. Comput., 2025)

Compatible Conservation Laws and Discrete Counterparts for the Time-Fractional Nonlinear Schrödinger Equation. - Pin Lyu; Hong-lin Liao; Seakweng Vong (J. Sci. Comput., 2025)