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We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we(More)
B-spline functions and curves are impor tant tools nowadays in many fields of mathematics and engineering, and in the meant ime there exist a lot of recursion formulas for the computa t ion of a B-spline's values (e.g. [2,5]), its derivative (e.g. [2,10]), its partial derivative w.r.t, the knots (e.g. [12,19]) and for knot insertion (e.g. [1]). A compend(More)
We introduce a family of trigonometric polynomials, denoted as Stancu polynomials, which contains the trigonometric Lagrange and Bernstein polynomials. This family depends only on one real parameter, denoted as design parameter. Our approach works for curves as well as for surfaces over triangles. The resulting Stancu curves respectively surfaces therefore(More)
It is a well-known fact that the classical (i.e. polynomial) divided difference of orderm, when applied to a functiong, converges to themth-derivative of this function, if the evaluation points all collapse to a single one. In the first part of this paper we shall sharpen this result in the sense that we prove the existence of an asymptotic expansion with(More)
One of the fundamental results in spline interpolation theory is the famous Schoenberg-Whitney Theorem, which completely characterizes those distributions of interpolation points which admit unique interpolation by splines. However, until now there exists no iterative algorithm for the explicit computation of the interpolating spline function, and the only(More)
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