The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems

DOI10.1016/j.matcom.2020.10.010OpenAlexW3094330705MaRDI QIDQ1998343

Demetriana Tappoura, Andreas Karageorghis, Ching-Shyang Chen

Publication date: 6 March 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2020.10.010

zbMATH Keywords

centresshape parameterKansa RBF method

Mathematics Subject Classification ID

Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (11)

Effective condition number for the selection of the RBF shape parameter with the fictitious point method ⋮ Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel ⋮ Enhanced shifted Tchebyshev operational matrix of derivatives: two spectral algorithms for solving even-order BVPs ⋮ A polynomial-augmented RBF collocation method for fourth-order boundary value problems ⋮ A Fully Implicit Method Using Nodal Radial Basis Functions to Solve the Linear Advection Equation ⋮ A time-efficient variable shape parameter Kansa-radial basis function method for the solution of nonlinear boundary value problems ⋮ An efficient localized meshless technique for approximating nonlinear sinh-Gordon equation arising in surface theory ⋮ Kansa RBF collocation method with auxiliary boundary centres for high order BVPs ⋮ The quasi-optimal radial basis function collocation method: a technical note ⋮ Numerical solution of optimal control of atherosclerosis using direct and indirect methods with shooting/collocation approach ⋮ Training RBF neural networks for the solution of elliptic boundary value problems

Uses Software

• Matlab
• COMSOL

Cites Work

• Unnamed Item
• Unnamed Item
• The MFS for the solution of harmonic boundary value problems with non-harmonic boundary conditions
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Meshfree explicit local radial basis function collocation method for diffusion problems
• The black-box fast multipole method
• The method of fundamental solutions for elliptic boundary value problems
• Observations on the behavior of radial basis function approximations near boundaries
• Radial basis function methods for the Rosenau equation and other higher order PDEs
• Fast method of approximate particular solutions using Chebyshev interpolation
• Improved Kansa RBF method for the solution of nonlinear boundary value problems
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• The sample solution approach for determination of the optimal shape parameter in the multiquadric function of the Kansa method
• Scattered Data Interpolation: Tests of Some Method
• On the Selection of a Good Shape Parameter of the Localized Method of Approximated Particular Solutions
• Improved RBF Collocation Methods for Fourth Order Boundary Value Problems
• A fast algorithm for particle simulations

This page was built for publication: The Kansa RBF method with auxiliary boundary centres for fourth order boundary value problems