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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)