Collocation discretizations of the transport equation with radial basis functions.

DOI10.1016/S0096-3003(02)00472-1zbMath1037.65102OpenAlexW1985235782MaRDI QIDQ1412432

Joseph D. Ward, Francis J. Narcowich, Rudolph Alexander Lorentz

Publication date: 25 November 2003

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00472-1

zbMATH Keywords

stabilityerror estimatesradial basis functionstransport equationcollocationadvection equationbackward Euler schemehyperbolic PDEscovnergence

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (10)

A meshfree method for the numerical solution of the RLW equation ⋮ A computational modeling of the behavior of the two-dimensional reaction-diffusion Brusselator system ⋮ Stability of radial basis collocation method for transient dynamics ⋮ An adaptive least-squares collocation radial basis function method for the HJB equation ⋮ Numerical solutions of KdV equation using radial basis functions ⋮ Dispersion and stability properties of radial basis collocation method for elastodynamics ⋮ Order-preserving derivative approximation with periodic radial basis functions ⋮ A NEW BACKUS–GILBERT MESHLESS APPROXIMATION METHOD FOR INITIAL-BOUNDARY VALUE PARTIAL DIFFERENTIAL EQUATIONS ⋮ Two-dimensional contaminant transport modeling using meshfree point collocation method (PCM) ⋮ A Computational Meshfree Technique for the Numerical Solution of the Two-Dimensional Coupled Burgers' Equations

Cites Work

• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold
• Solving partial differential equations by collocation using radial basis functions
• A multiquadric interpolation method for solving initial value problems
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Approximation by periodic spline interpolants on uniform meshes
• Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$
• Meshless Galerkin methods using radial basis functions
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
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