Norms of inverses for matrices associated with scattered data
Curves and surfaces
An efficient numerical scheme for Burgers' equation
Applied Mathematics and Computation
A unified theory of radial basis functions Native Hilbert spaces for radial basis functions II
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Lp-error estimates for "shifted" surface spline interpolation on Sobolev space
Mathematics of Computation
An approximate method for numerical solution of fractional differential equations
Signal Processing - Fractional calculus applications in signals and systems
Optimal constant shape parameter for multiquadric based RBF-FD method
Journal of Computational Physics
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The purpose of this paper is to investigate the collocation method based on Multiquadric (MQ) radial basis functions (RBFs) for fractional differential equations (FDEs). In the process of doing this, a scattered data RBF interpolation is considered. A posterior error bound for the smooth solutions of FDEs in the proposed method is established in the L"2 norm, using an alternate characterization of the native space. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method.