Adaptive Gaussian radial basis function methods for initial value problems: construction and comparison with adaptive multiquadric radial basis function methods

DOI10.1016/j.cam.2020.113036zbMath1455.65107OpenAlexW3037629987MaRDI QIDQ2195928

Jae-Hun Jung, Jiaxi Gu

Publication date: 28 August 2020

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.2020.113036

zbMATH Keywords

finite difference methodinitial value problemsGaussian radial basis functions

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Spline approximation (41A15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Finite difference and finite volume methods for ordinary differential equations (65L12) Numerical radial basis function approximation (65D12)

Related Items (3)

Coupled Kansa and hybrid optimization methodological approach for Kolmogorov-Feller equations ⋮ Construction and comparative study of second order time stepping methods based on IQ and IMQ-RBFs ⋮ Consistent, non-oscillatory RBF finite difference solutions to boundary layer problems for any degree on uniform grids

Cites Work

• A RBF-WENO finite volume method for hyperbolic conservation laws with the monotone polynomial interpolation method
• Radial basis function ENO and WENO finite difference methods based on the optimization of shape parameters
• Some observations regarding interpolants in the limit of flat radial basis functions
• 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
• An adaptive error inhibiting block one-step method for ordinary differential equations
• Adaptive radial basis function methods for initial value problems
• On choosing ``optimal shape parameters for RBF approximation
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation
• Interpolation by basis functions of different scales and shapes
• Convergence and stability in the numerical integration of ordinary differential equations
• Radial Basis Functions

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