Kansa RBF collocation method with auxiliary boundary centres for high order BVPs

DOI10.1016/j.cam.2021.113680zbMath1478.65135OpenAlexW3169100765MaRDI QIDQ2043188

Lionel Amuzu, Andreas Karageorghis, Ching-Shyang Chen

Publication date: 29 July 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113680

zbMATH Keywords

radial basis functionscollocationmultiquadricsKansa methodhigh order partial differential equationsfictitious point method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Higher-order elliptic equations (35J30) Fictitious domain methods for boundary value problems involving PDEs (65N85) Numerical radial basis function approximation (65D12)

Related Items (3)

A D-N alternating algorithm for exterior 3-D problem with ellipsoidal artificial boundary ⋮ Random sampling and unisolvent interpolation by almost everywhere analytic functions ⋮ Fictitious centre RBF method for high order BVPs in multiply connected domains

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions
• An unconditionally energy-stable method for the phase field crystal equation
• Efficient MFS algorithms for inhomogeneous polyharmonic problems
• Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation
• A random variable shape parameter strategy for radial basis function approximation methods
• Partial differential equations. 3rd ed
• Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics
• Doubly stochastic radial basis function methods
• Improved Kansa RBF method for the solution of nonlinear boundary value problems
• A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains
• An interval for the shape parameter in radial basis function approximation
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• On unsymmetric collocation by radial basis functions
• Results on meshless collocation techniques
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems
• The sample solution approach for determination of the optimal shape parameter in the multiquadric function of the Kansa method
• On the sinc-Galerkin method for triharmonic boundary-value problems
• Space of \(C^2\)-smooth geometrically continuous isogeometric functions on two-patch geometries
• On the search of the shape parameter in radial basis functions using univariate global optimization methods
• An adaptive LOOCV-based refinement scheme for RBF collocation methods over irregular domains
• A semi-Lagrangian meshless framework for numerical solutions of two-dimensional sloshing phenomenon
• Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates
• Variable shape parameter Kansa RBF method for the solution of nonlinear boundary value problems
• On choosing ``optimal shape parameters for RBF approximation
• Isogeometric analysis of high order partial differential equations on surfaces
• Maximum theorems for solutions of higher order elliptic equations
• Scattered Data Interpolation: Tests of Some Method
• Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains
• A Comparison of Popular Point Configurations on $\mathbb{S}^2$

This page was built for publication: Kansa RBF collocation method with auxiliary boundary centres for high order BVPs