Solving biharmonic equation using the localized method of approximate particular solutions

DOI10.1080/00207160.2013.862525zbMath1306.65280OpenAlexW2027305292MaRDI QIDQ2935395

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Publication date: 29 December 2014

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

Full work available at URL: https://doi.org/10.1080/00207160.2013.862525

zbMATH Keywords

collocation methodfinite difference methodnumerical examplesradial basis functionsbiharmonic equationPoisson equationlocalized method of approximate particular solutionslocalized Kansa's method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for higher-order elliptic equations (35J40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (10)

Numerical solution of stochastic elliptic partial differential equations using the meshless method of radial basis functions ⋮ The local Kansa's method for solving Berger equation ⋮ Higher order approximation of biharmonic problem using the WEB-spline based mesh-free method ⋮ Solving Nonlinear Elliptic PDEs in 2D and 3D Using Polyharmonic Splines and Low-Degree of Polynomials ⋮ Solving Fourth-Order PDEs using the LMAPS ⋮ The Modified Localized Method of Approximated Particular Solutions for Linear and Nonlinear Convection-Diffusion-Reaction PDEs ⋮ Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains ⋮ The LMAPS for solving fourth-order PDEs with polynomial basis functions ⋮ Generalized finite integration method with Volterra operator for multi-dimensional biharmonic equations ⋮ Solving biharmonic equation as an optimal control problem using localized radial basis functions collocation method

Cites Work

• The comparison of three meshless methods using radial basis functions for solving fourth-order partial differential equations
• A localized approach for the method of approximate particular solutions
• Meshfree explicit local radial basis function collocation method for diffusion problems
• A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow
• A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles
• Local multiquadric approximation for solving boundary value problems
• A mixed finite volume element method based on rectangular mesh for biharmonic equations
• Fast multipole method for the biharmonic equation in three dimensions
• The method of approximate particular solutions for solving certain partial differential equations
• THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS
• A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
• Multidimensional binary search trees used for associative searching
• Multigrid Solution of Automatically Generated High-Order Discretizations for the Biharmonic Equation
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Discontinuous Galerkin methods for the biharmonic problem

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