Fully-discrete energy-preserving scheme for the space-fractional Klein–Gordon equation via Lagrange multiplier type scalar auxiliary variable approach

An analytic study on the approximate solution of a nonlinear time‐fractional Cauchy reaction–diffusion equation with the Mittag–Leffler law

(2021) Kamyar Hosseini et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense

(2021) Kamyar Hosseini et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

A family of effective structure-preserving schemes with second-order accuracy for the undamped sine–Gordon equation

(2021) Jun-Ya Wang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping

(2021) Dongdong Hu et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

A fourth-order exponential wave integrator Fourier pseudo-spectral method for the Klein-Gordon equation

(2020) Bingquan Ji et al.   APPLIED MATHEMATICS LETTERS

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

(2020) Yayun Fu et al.   APPLIED NUMERICAL MATHEMATICS

A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition

(2020) Xiujun Cheng et al.   APPLIED NUMERICAL MATHEMATICS

Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation

(2020) Yayun Fu et al.   APPLIED NUMERICAL MATHEMATICS

Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations

(2020) Hong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

(2020) Chaolong Jiang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Symplectic‐preserving Fourier spectral scheme for space fractional Klein–Gordon–Schrödinger equations

(2020) Junjie Wang   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations

(2020) Chaolong Jiang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Efficient and linear schemes for anisotropic Cahn–Hilliard model using the Stabilized-Invariant Energy Quadratization (S-IEQ) approach

(2019) Zhen Xu et al.   COMPUTER PHYSICS COMMUNICATIONS

A family of second-order energy-stable schemes for Cahn–Hilliard type equations

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An unconditionally energy stable scheme for simulating wrinkling phenomena of elastic thin films on a compliant substrate

(2019) Qiong-Ao Huang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Linearly Implicit and Local Energy-Preserving Scheme for the Sine-Gordon Equation Based on the Invariant Energy Quadratization Approach

(2019) Chaolong Jiang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Conservative Local Discontinuous Galerkin method for the fractional Klein-Gordon-Schrödinger system with generalized Yukawa interaction

(2019) P. Castillo et al.   NUMERICAL ALGORITHMS

A linear, symmetric and energy-conservative scheme for the space-fractional Klein–Gordon–Schrödinger equations

(2019) Ying Wang et al.   APPLIED MATHEMATICS LETTERS

An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy†

(2019) Qiong-Ao Huang   Communications in Computational Physics

A New Multi-Component Diffuse Interface Model with Peng-Robinson Equation of State and its Scalar Auxiliary Variable (SAV) Approach

(2019) Zhonghua Qiao sci   Communications in Computational Physics

Long Time Error Analysis of Finite Difference Time Domain Methods for the Nonlinear Klein-Gordon Equation with Weak Nonlinearity

(2019) Weizhu Bao   Communications in Computational Physics

Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions

(2019) Wenjun Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates

(2019) Qingqu Zhuang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime

(2019) Weizhu Bao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Fourier spectral method for the nonlinear coupled space fractional Klein‐Gordon‐Schrödinger equations

(2019) Junqing Jia et al.   ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach

(2018) Xiaofeng Yang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

An efficient Hamiltonian numerical model for a fractional Klein–Gordon equation through weighted-shifted Grünwald differences

(2018) Ahmed S. Hendy et al.   JOURNAL OF MATHEMATICAL CHEMISTRY

A numerically efficient and conservative model for a Riesz space-fractional Klein–Gordon–Zakharov system

(2018) A.S. Hendy et al.   Communications in Nonlinear Science and Numerical Simulation

Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

(2017) Xiaofeng Yang et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Analysis and Approximation of a Fractional Cahn--Hilliard Equation

(2017) Mark Ainsworth et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Uniqueness and approximation of solution for fractional Bagley–Torvik equations with variable coefficients

(2016) H. M. Wei et al.   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations

(2016) Dong Li et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime

(2014) Weizhu Bao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Asymptotic preserving schemes for the Klein–Gordon equation in the non-relativistic limit regime

(2013) Erwan Faou et al.   NUMERISCHE MATHEMATIK

The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation

(2013) Fanhai Zeng et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

(2011) Changpin Li et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS