A new meshless collocation method for partial differential equations

DOI10.1002/cnm.1055zbMath1155.65080OpenAlexW2049589407MaRDI QIDQ3546178

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Publication date: 18 December 2008

Published in: Communications in Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cnm.1055

zbMATH Keywords

stabilitywave equationconsistencycondition numberBurgers' equationPoisson equationshape functionssearch algorithmmeshless collocation methodnearest neighbor algorithmscattered data modelingstencil selectionGauss-Jordan pivot method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (6)

The improved element-free Galerkin method for three-dimensional wave equation ⋮ Meshless local Petrov-Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation ⋮ Semi-meshless stencil selection for anisotropic point distributions ⋮ A high order meshless method with compact support ⋮ Adaptive meshless centres and RBF stencils for Poisson equation ⋮ On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations

Cites Work

• Positivity conditions in meshless collocation methods
• An efficient numerical scheme for Burger equation
• Meshless methods: An overview and recent developments
• \(hp\)-meshless cloud method
• Multistep scattered data interpolation using compactly supported radial basis functions
• Multiresolution methods in scattered data modelling.
• Meshfree collocation solution of boundary value problems via interpolating moving least squares
• Generation of Difference and Error Formulae of Arbitrary Consistency Order on an Unstructured Grid
• How we solve PDEs
• Unnamed Item

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