Construction of cubic splines for interpolating functional dependencies and processing the results of experimental studies

Abstract

Algorithms for constructing cubic splines with different boundary conditions have been developed: 1. The second derivative takes arbitrary values at the ends of the spline. A special case is the “natural spline”, when the second derivative at its ends is equal to zero. 2. At one end of the spline, the first derivative is given, and at the opposite end – the second derivative. 3. The first derivative is given at the two ends of the spline without any restrictions on the second derivatives. The proposed methods were tested on the example of interpolation of the function 10x sin xe −x for the interval [0, 1]. The relative calculation error for the number of nodes n = 10 was about 10−2. With an increase in the number of nodes to 1000 and 10000, the error increases, respectively, to 10−6 and 10−7 −10−8. It is shown that a number of problems with other boundary conditions can be solved using the proposed methods. The considered algorithms can be used for interpolating functional dependencies and processing the results of experimental studies, represented as a discrete set of pairs of numbers.