An engineer's guide to soliton phenomena: Application of the finite element method
Computer Methods in Applied Mechanics and Engineering
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
Numerical simulation of quasi-periodic solutions of the sine-Gordon equation
Proceedings of the conference on The nonlinear Schrodinger equation
SIAM Journal on Numerical Analysis
A decomposition method for solving the nonlinear Klein-Gordon equation
Journal of Computational Physics
Journal of Computational Physics
An initial-boundary value problem of a nonlinear Klein-Gordon equation
Applied Mathematics and Computation
Non-perturbative solution of the Klein-Gordon-Zakharov equation
Applied Mathematics and Computation
On the numerical solution of the sine-Gordon equation II: performance of numerical schemes
Journal of Computational Physics
A family of parametric finite-difference methods for the solution of the sine-Gordon equation
Applied Mathematics and Computation
Solitons in Josephson junctions
Physica D - Special issue on nonlinear waves and solitons in physical systems
The sine-Gordon equation in the finite line
Applied Mathematics and Computation
A third order numerical scheme for the two-dimensional sine-Gordon equation
Mathematics and Computers in Simulation
Tension spline solution of nonlinear sine-Gordon equation
Numerical Algorithms
Mathematical and Computer Modelling: An International Journal
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A numerical scheme arising from the use of a fourth order rational approximants to the matrix-exponential term in a three-time level recurrence relation is proposed for the numerical solution of the one-dimensional sine-Gordon (SG) equation already known from the bibliography. The method for its implementation uses a predictor-corrector scheme in which the corrector is accelerated by using the already evaluated corrected values modified predictor-corrector scheme. For the implementation of the corrector, in order to avoid extended matrix evaluations, an auxiliary vector was successfully introduced. Both the predictor and the corrector schemes are analysed for stability. The predictor-corrector/modified predictor-corrector (P-C/MPC) schemes are tested on single and soliton doublets as well as on the collision of breathers and a comparison of the numerical results with the corresponding ones in the bibliography is made. Finally, conclusions for the behaviour of the introduced MPC over the standard P-C scheme are derived.