@inproceedings{bd0ce8c0a1d64793b587357404d7e152,

title = "Construction of non-polynomial splines of the first level with fourth order of approximation",

abstract = "Interpolation using Hermite polynomial cubic splines is well known and often used. Here we propose an approximation with the non-polynomial splines with the fourth order of approximation. The splines uses the values of the function and the first derivative of the function in the nodes. We call the approximation as first level approximation because it uses the first derivative of the function. This approximation has the properties of polynomial and trigonometric functions. Here we also have constructed a non-polynomial interpolating spline which has continuous the first and second derivative. This approximation uses the values of the function at the nodes and the values of the first derivative of the function at the ends of the interval [a, b]. Estimates of the approximations are given and the constants included in them are calculated. Numerical examples are given.",

author = "Burova, {I. G.}",

note = "Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference date: 23-09-2019 Through 28-09-2019",

year = "2020",

month = nov,

day = "24",

doi = "10.1063/5.0031655",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

editor = "Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Simos, {Theodore E.} and Charalambos Tsitouras",

booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019",

address = "United States",

}