A fourth order numerical scheme for the one-dimensional sine-Gordon equation

DOI10.1080/00207160701473939zbMath1145.65053OpenAlexW1974607468MaRDI QIDQ3518555

A. G. Bratsos

Publication date: 8 August 2008

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701473939

zbMATH Keywords

stabilitynumerical resultspredictor-corrector methodsolitonfinite-difference methodsine-Gordon equationfourth order rational approximants

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Soliton equations (35Q51)

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Cites Work

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• An engineer's guide to soliton phenomena: Application of the finite element method
• On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes
• Two energy conserving numerical schemes for the sine-Gordon equation
• A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation
• Analysis of four numerical schemes for a nonlinear Klein-Gordon equation
• Numerical simulation of quasi-periodic solutions of the sine-Gordon equation
• Numerical solution of the sine-Gordon equation
• Numerical solution of a nonlinear Klein-Gordon equation
• A family of parametric finite-difference methods for the solution of the sine-Gordon equation
• Derivation of the discrete conservation laws for a family of finite difference schemes
• Non-perturbative solution of the Klein-Gordon-Zakharov equation
• An initial-boundary value problem of a nonlinear Klein-Gordon equation
• The sine-Gordon equation in the finite line
• A decomposition method for solving the nonlinear Klein-Gordon equation
• On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds
• The solution of the sine-gordon equation using the method of lines
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Solitary wave solutions of nonlinear wave equations
• A model unified field equation
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Product Approximation for Nonlinear Klein-Gordon Equations
• Solitary Wave Collisions
• Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
• A predictor--corrector scheme for the sine-Gordon equation