Open AccessApproximations With Polynomial, Trigonometric, Exponential Splines of the Third Order and Boundary Value Problem
Author(s) -
И. Г. Бурова,
E. F. Muzafarova
Publication year - 2020
Publication title -
international journal of circuits, systems and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.156
H-Index - 13
ISSN - 1998-4464
DOI - 10.46300/9106.2020.14.61
Subject(s) - mathematics , trigonometry , boundary value problem , polynomial , computation , exponential function , trigonometric polynomial , box spline , boundary (topology) , mathematical analysis , algorithm , spline interpolation , statistics , bilinear interpolation
This paper is devoted to the construction of localapproximations of functions of one and two variables using thepolynomial, the trigonometric, and the exponential splines. Thesesplines are useful for visualizing flows of graphic information.Here, we also discuss the parallelization of computations. Someattention is paid to obtaining two-sided estimates of theapproximations using interval analysis methods. Particularattention is paid to solving the boundary value problem by usingthe polynomial splines and the trigonometric splines of the thirdand fourth order approximation. Using the considered splines,formulas for a numerical differentiation are constructed. Theseformulas are used to construct computational schemes for solvinga parabolic problem. Questions of approximation and stability ofthe obtained schemes are considered. Numerical examples arepresented.