Meshless singular boundary method for nonlinear sine-Gordon equation

DOI10.1155/2018/6460480zbMath1427.65288OpenAlexW2855980131MaRDI QIDQ1721257

Yun Ji

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/6460480

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

Singular boundary method: a review and computer implementation aspects, Solutions of two-dimensional nonlinear sine-Gordon equation via triple Laplace transform coupled with iterative method, Numerical solution of two-dimensional nonlinear sine-Gordon equation using localized method of approximate particular solutions

Cites Work

• Unnamed Item
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• Lagrange interpolation and modified cubic B-spline differential quadrature methods for solving hyperbolic partial differential equations with Dirichlet and Neumann boundary conditions
• A method of fundamental solutions without fictitious boundary
• Singular boundary method for modified Helmholtz equations
• 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
• 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
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear elements
• Finite element approximation to two-dimensional sine-Gordon solitons
• Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions
• Radial basis functions as approximate particular solutions: Review of recent progress
• Meshless singular boundary methods for biharmonic problems
• The element-free Galerkin method for the nonlinear \(p\)-Laplacian equation
• A generalized element-free Galerkin method for Stokes problem
• Numerical solutions of a damped sine-Gordon equation in two space variables
• 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
• Analysis of the complex moving least squares approximation and the associated element-free Galerkin method
• Meshless numerical analysis of a class of nonlinear generalized Klein-Gordon equations with a well-posed moving least squares approximation
• 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
• Numerical solution of Klein-Gordon and sine-Gordon equations by meshless method of lines
• A numerical scheme based on differential quadrature method for numerical simulation of nonlinear Klein-Gordon equation
• Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method
• A moving Kriging‐based MLPG method for nonlinear Klein–Gordon equation