Splines in physicochemical studies of liquid binary mixtures - Iwanow, Zdzisław; Bauer, Jacek; Jelińska-Kazimierczuk, Małgorzata (Computer Assisted Methods in Engineering and Science, 2023)
Physicochemical studies of the organic-water mixtures show that their properties are not linear functions of their concentration but depend on the mixture composition in various ways. The evaluation of the measurement results requires an interpolation of the experimental data and the derivatives of a mixture property with respect to concentration should be known as well. The results of measurements are disturbed by experimental error which causes the scatter of the approximated function values and oscillations of the approximating function derivatives. In the paper an application of the 3rd degree splines for the calculation of derivative and the interpolation for a non-uniform mesh are considered. Smoothing methods of an approximating function by means of splines are proposed. Some numerical examples illustrating the efficiency of the smoothing method and its applications are presented.