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Approximation of solutions of nonlinear initial-value problems by B-spline functions

Krzysztof Wesołowski (2011)

Banach Center Publications

This note is motivated by [GGG], where an algorithm finding functions close to solutions of a given initial value-problem has been proposed (this algorithm has been recalled in Theorem 2.2). In this paper we present a commonly used definition and basic facts concerning B-spline functions and use them to improve the mentioned algorithm. This leads us to a better estimate of the Cauchy problem solution under some additional assumption on f appearing in the Cauchy problem. We also estimate the accuracy...

Biquadratic splines interpolating mean values

Jiří Kobza, Jan Mlčák (1994)

Applications of Mathematics

Continuity conditions for a biquadratic spline interpolating given mean values in terms of proper parameters are given. Boundary conditions determining such a spline and the algorithm for computing local parameters for the given data are studied. The notion of the natural spline and its extremal property is mentioned.

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