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In this paper, we use a kind of univariate multiquadric (MQ) quasi-interpolation to solve partial differential equation (PDE). We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the… (More)
1 The work was done during the author's visit to GG ottingen under support of a DAAD-Wong fellowship. Abstract: Under mild additional assumptions this paper constructs quasi-interpolants in the form f h (x) = +1 X j=1 f(hj)' h x h j ; x 2 IR; h > 0 (0.1) with approximation order`1, where ' h (x) is a linear combination of translates (x jh) of a function in… (More)
In this paper, we study several radial basis function approximation schemes in Sobolev spaces. We obtain an optional error estimate by using a class of smoothing operators. We also discussed sufficient conditions for the smoothing operators to attain the desired approximation order. We then construct the smoothing operators by some compactly supported… (More)
Based on the definition of MQ-B-Splines, this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details. And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.