Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain

Authors:
Houde Han;Zhiwen Zhang
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China
Venue:
Journal of Computational Physics
Year:
2008

Citing 17
Cited 5

Analysis of four numerical schemes for a nonlinear Klein-Gordon equation

Applied Mathematics and Computation
Two energy conserving numerical schemes for the sine-Gordon equation

Applied Mathematics and Computation
Derivation of the discrete conservation laws for a family of finite difference schemes

Applied Mathematics and Computation
Exact nonreflecting boundary conditions for the time dependent wave equation

SIAM Journal on Applied Mathematics
Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation

SIAM Journal on Numerical Analysis
Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation

SIAM Journal on Numerical Analysis
Statistical mechanics of double sinh-Gordon kinks

Physica D - Special issue on nonlinear waves and solitons in physical systems
Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling

Proceedings of the on Numerical methods for differential equations
Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation

SIAM Journal on Numerical Analysis
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime

Journal of Computational Physics
Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes

SIAM Journal on Scientific Computing
Exact boundary condition for time-dependent wave equation based on boundary integral

Journal of Computational Physics
Local spectral time splitting method for first- and second-order partial differential equations

Journal of Computational Physics
Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations

Journal of Computational Physics
The splitting finite-difference time-domain methods for Maxwell's equations in two dimensions

Journal of Computational and Applied Mathematics
Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems

Journal of Computational Physics
Numerical Solution to the Sine-Gordon Equation Defined on the Whole Real Axis

SIAM Journal on Scientific Computing

Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions

Journal of Computational and Applied Mathematics
Numerical solution of the nonlinear Klein-Gordon equation

Journal of Computational and Applied Mathematics
Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains

Mathematics and Computers in Simulation
Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings

Journal of Computational Physics
Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in R2

Journal of Scientific Computing

Quantified Score

Hi-index	31.45

Visualization

Abstract

The numerical solution of the one-dimensional nonlinear Klein-Gordon equation on an unbounded domain is studied in this paper. Split local absorbing boundary (SLAB) conditions are obtained by the operator splitting method, then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several numerical examples are provided to show the advantages and effectiveness of the given method, and some interesting collision behaviors are also observed.