Meshless numerical analysis of a class of nonlinear generalized Klein-Gordon equations with a well-posed moving least squares approximation

DOI10.1016/j.apm.2017.03.063zbMath1480.65265OpenAlexW2604406592MaRDI QIDQ2293855

Xiao-Lin Li

Publication date: 5 February 2020

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2017.03.063

zbMATH Keywords

convergencesolitonsine-Gordonmeshlessnonlinear generalized Klein-Gordon equationwell-posed moving least squares approximation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (11)

Approximate analytic solutions of two-dimensional nonlinear Klein-Gordon equation by using the reduced differential transform method ⋮ Development of non polynomial spline and New B-spline with application to solution of Klein-Gordon equation ⋮ An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation ⋮ Augmented moving least squares approximation using fundamental solutions ⋮ Fast Computing Approaches Based on a Bilinear Pseudo-Spectral Method for Nonlinear Acoustic Wave Equations ⋮ Meshless singular boundary method for nonlinear sine-Gordon equation ⋮ A wavelet method to solve nonlinear variable-order time fractional 2D Klein-Gordon equation ⋮ Numerical solution of sine-Gordon equation with the local kriging meshless method ⋮ A computational method for solving variable-order fractional nonlinear diffusion-wave equation ⋮ A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations ⋮ Numerical solution of two-dimensional nonlinear sine-Gordon equation using localized method of approximate particular solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The numerical solution of the nonlinear Klein-Gordon and sine-Gordon equations using the Chebyshev tau meshless method
• Numerical solution of one-dimensional Sine-Gordon equation using high accuracy multiquadric quasi-interpolation
• Analyzing two-dimensional sine-Gordon equation with the mesh-free reproducing kernel particle Ritz method
• On the stability of the moving least squares approximation and the element-free Galerkin method
• Collocation and finite difference-collocation methods for the solution of nonlinear Klein-Gordon equation
• Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation
• Tension spline approach for the numerical solution of nonlinear Klein-Gordon equation
• Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
• Meshless Galerkin algorithms for boundary integral equations with moving least square approximations
• One and two soliton solutions for the sinh-Gordon equation in (1+1), (2+1) and (3+1) dimensions
• New travelling wave solutions to the Boussinesq and the Klein-Gordon equations
• Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations
• The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation
• Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation
• Error estimates for the moving least-square approximation and the element-free Galerkin method in \(n\)-dimensional spaces
• Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• Numerical study of \(2+1\) dimensional sine-Gordon solitons
• Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear elements
• A boundary element-free method (BEFM) for two-dimensional potential problems
• A Galerkin boundary node method and its convergence analysis
• Finite element approximation to two-dimensional sine-Gordon solitons
• An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations
• The numerical solution of the two-dimensional sinh-Gordon equation via three meshless methods
• Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method
• The improved moving least-square Ritz method for the one-dimensional sine-Gordon equation
• Numerical solutions of a damped sine-Gordon equation in two space variables
• A new implementation of the element free Galerkin method
• Numerical simulation of two-dimensional sine-Gordon solitons by differential quadrature method
• Analysis and application of the element-free Galerkin method for nonlinear sine-Gordon and generalized sinh-Gordon equations
• Meshless analysis and applications of a symmetric improved Galerkin boundary node method using the improved moving least-square approximation
• A Dufort-Frankel difference scheme for two-dimensional sine-Gordon equation
• The solution of the two-dimensional sine-Gordon equation using the method of lines
• Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
• A meshless RBF method for computing a numerical solution of unsteady Burgers'-type equations
• A moving least square reproducing polynomial meshless method
• Numerical solution of Klein-Gordon and sine-Gordon equations by meshless method of lines
• Auxiliary equation method and new solutions of Klein-Gordon equations
• The \(\tan h\) method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations
• The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation
• On generalized moving least squares and diffuse derivatives
• Meshfree Particle Methods
• Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems
• Kadomstev-Petviashvile and two-dimensional sine-Gordon equations: reduction to Painleve transcendents
• Surfaces Generated by Moving Least Squares Methods
• The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations

This page was built for publication: Meshless numerical analysis of a class of nonlinear generalized Klein-Gordon equations with a well-posed moving least squares approximation