Radial basis functions for solving differential equations: ill-conditioned matrices and numerical stability

DOI10.1016/j.camwa.2015.11.013zbMath1443.65106OpenAlexW2187049642MaRDI QIDQ2006610

Manfred R. Trummer, Sarah E. Huber

Publication date: 11 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.11.013

zbMATH Keywords

radial basis functionsdifferential equationsboundary layersill-conditioning

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15)

Related Items (3)

A higher‐order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin‐boundary conditions ⋮ Consistent, non-oscillatory RBF finite difference solutions to boundary layer problems for any degree on uniform grids ⋮ Direct and integrated radial functions based quasilinearization schemes for nonlinear fractional differential equations

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• Error estimates and condition numbers for radial basis function interpolation
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• Effective condition number for finite difference method
• On choosing ``optimal shape parameters for RBF approximation
• Effectively Well-Conditioned Linear Systems
• Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems

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