High accurate finite differences based on RBF interpolation and its application in solving differential equations

DOI10.1007/s10915-018-0684-zzbMath1410.65416OpenAlexW2790790201MaRDI QIDQ1785514

Junna Duan, Renzhong Feng

Publication date: 28 September 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-018-0684-z

zbMATH Keywords

interpolationRBFradial basis functiontruncation errorapproximation errorLagrange form

Mathematics Subject Classification ID

Numerical interpolation (65D05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

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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
• RBF-FD formulas and convergence properties
• Some observations regarding interpolants in the limit of flat radial basis functions
• Interpolation in the limit of increasingly flat radial basis functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• On choosing ``optimal shape parameters for RBF approximation
• Scattered node compact finite difference-type formulas generated from radial basis functions
• Local error estimates for radial basis function interpolation of scattered data
• Interpolation in Two Dimensions—A New Technique
• Error estimates of local multiquadric-based differential quadrature (LMQDQ) method through numerical experiments
• Scattered Data Approximation
• Unnamed Item

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