Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation with weak nonlinearity

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

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

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

Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime

(2017) Weizhu Bao et al.   MATHEMATICS OF COMPUTATION

Fourth-order compact and energy conservative scheme for solving nonlinear Klein-Gordon equation

(2017) Yuesheng Luo et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

A uniformly accurate (UA) multiscale time integrator Fourier pseudospectral method for the Klein–Gordon–Schrödinger equations in the nonrelativistic limit regime

(2016) Weizhu Bao et al.   NUMERISCHE MATHEMATIK

Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

(2016) WeiZhu Bao et al.   Science China-Mathematics

On Time-Splitting Pseudospectral Discretization for Nonlinear Klein-Gordon Equation in Nonrelativistic Limit Regime

(2016) Xuanchun Dong et al.   Communications in Computational Physics

High-order difference scheme for the solution of linear time fractional klein-gordon equations

(2014) Akbar Mohebbi et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Uniformly accurate numerical schemes for highly oscillatory Klein–Gordon and nonlinear Schrödinger equations

(2014) Philippe Chartier et al.   NUMERISCHE MATHEMATIK

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

A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term

(2013) Akbar Mohebbi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions

(2013) Tingchun Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An Exponential Wave Integrator Sine Pseudospectral Method for the Klein--Gordon--Zakharov System

(2013) Weizhu Bao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation

(2012) Weizhu Bao et al.   MATHEMATICS OF COMPUTATION

Analysis and comparison of numerical methods for the Klein–Gordon equation in the nonrelativistic limit regime

(2011) Weizhu Bao et al.   NUMERISCHE MATHEMATIK

Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein–Gordon equation

(2010) Mehdi Dehghan et al.   COMPUTER PHYSICS COMMUNICATIONS

Long-time existence for semi-linear Klein–Gordon equations on tori

(2010) Daoyuan Fang et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus

(2009) J.-M. Delort   JOURNAL D ANALYSE MATHEMATIQUE

Fourth-order compact solution of the nonlinear Klein-Gordon equation

(2009) Mehdi Dehghan et al.   NUMERICAL ALGORITHMS

An implicit fourth-order compact finite difference scheme for one-dimensional Burgers’ equation

(2008) Wenyuan Liao   APPLIED MATHEMATICS AND COMPUTATION

Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations

(2008) David Cohen et al.   NUMERISCHE MATHEMATIK

New travelling wave solutions to the Boussinesq and the Klein–Gordon equations

(2006) Abdul-Majid Wazwaz   Communications in Nonlinear Science and Numerical Simulation