Tension spline solution of nonlinear sine-Gordon equation

DOI10.1007/s11075-010-9377-xzbMath1206.65214OpenAlexW1966021600MaRDI QIDQ621787

Reza Mohammadi, Jalil Rashidinia

Publication date: 28 January 2011

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-010-9377-x

zbMATH Keywords

stability analysisnumerical examplesfinite difference schemessine-Gordon equationnon-polynomial spline under tension

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40)

Related Items (21)

Sextic B-spline collocation method for solving Euler-Bernoulli beam models ⋮ Wave dynamics on networks: method and application to the sine-Gordon equation ⋮ A new numerical method based on non-polynomial spline in tension approximations for 1D quasilinear hyperbolic equations on a variable mesh ⋮ Numerical simulation of a class of nonlinear wave equations by lattice Boltzmann method ⋮ A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation ⋮ A new algorithm based on spline in tension approximation for 1D quasi-linear parabolic equations on a variable mesh ⋮ A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasi-linear hyperbolic equations ⋮ Fourth-order cubic B-spline collocation method for hyperbolic telegraph equation ⋮ Exponentially fitted methods for solving two-dimensional time fractional damped Klein-Gordon equation with nonlinear source term ⋮ Higher order scheme for two-dimensional inhomogeneous sine-Gordon equation with impulsive forcing ⋮ Numerical solution of nonlinear sine-Gordon equation by modified cubic B-spline collocation method ⋮ A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates ⋮ Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term ⋮ Spline solution of the generalized Burgers'-Fisher equation ⋮ An exponential spline solution of nonlinear Schrödinger equations with constant and variable coefficients ⋮ Quintic B-spline collocation approach for solving generalized Black-Scholes equation governing option pricing ⋮ Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method ⋮ Numerical solution of fractional sine-Gordon equation using spectral method and homogenization ⋮ On spatio-temporal dynamics of sine-Gordon soliton in nonlinear non-homogeneous media using fully implicit spectral element scheme ⋮ Cubic B-spline method for non-linear sine-Gordon equation ⋮ A new efficient fourth order collocation scheme for solving sine-Gordon equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes
• Numerical solution of sine-Gordon equation by variational iteration method
• Perturbation of topological solitons due to sine-Gordon equation and its type
• Two energy conserving numerical schemes for the 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
• The sine-Gordon equation in the finite line
• Numerical solutions of a damped sine-Gordon equation in two space variables
• On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds
• Homotopy analysis method for the sine-Gordon equation with initial conditions
• The solution of the sine-gordon equation using the method of lines
• A numerical method for the one-dimensional sine-Gordon equation
• A fourth order numerical scheme for the one-dimensional sine-Gordon equation
• The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equation
• 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
• A numerical method for one‐dimensional nonlinear Sine‐Gordon equation using collocation and radial basis functions
• High order implicit collocation method for the solution of two‐dimensional linear hyperbolic equation

This page was built for publication: Tension spline solution of nonlinear sine-Gordon equation