High order compact Alternating Direction Implicit method for the generalized sine-Gordon equation

Authors:
Mingrong Cui
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 8
Cited 3

Matrix analysis

Matrix analysis
Fourth-order approximations at first time level, linear stability analysis and the numerical solution of multidimensional second-order nonlinear hyperbolic equations in polar coordinates

Journal of Computational and Applied Mathematics
Implicit, compact, linearized &THgr;-methods with factorization for multidimentional reaction-diffusion equation

Applied Mathematics and Computation
Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme

Mathematics and Computers in Simulation
The solution of the two-dimensional sine-Gordon equation using the method of lines

Journal of Computational and Applied Mathematics
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

Compact alternating direction implicit method for two-dimensional time fractional diffusion equation

Journal of Computational Physics
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems

Journal of Computational Physics
A new fourth-order numerical algorithm for a class of nonlinear wave equations

Applied Numerical Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

High order compact Alternating Direction Implicit scheme is given for solving the generalized sine-Gordon equation in a two-dimensional rectangular domain. We apply the compact finite difference operators to obtain a fourth order discretization for the second order space derivatives, and we give a linearized three time level algorithm for solving the original nonlinear equation. Error estimate is given by the energy method. Numerical results are provided to verify the accuracy and efficiency of this algorithm.