Approximations of the sixth order with the polynomial and non-polynomial splines and variational-difference method

Результат исследований: Научные публикации в периодических изданияхстатья

Аннотация

This paper discusses the approximations with the local basis of the second level and the sixth order. We call it the approximation of the second level because in addition to the function values in the grid nodes it uses the values of the function, and the first and the second derivatives of the function. Here the polynomial approximations and the non-polynomial approximations of a special form are discussed. The non-polynomial approximation has the properties of polynomial and trigonometric functions. The approximations are twice continuously differentiable. Approximation theorems are given. These approximations use the values of the function at the nodes, the values of the first and the second derivatives of the function at the nodes, and the local basis splines. These basis splines are used for constructing variational-difference schemes for solving boundary value problems for differential equations. Numerical examples are given.

Язык оригиналаанглийский
Страницы (с-по)62-71
Число страниц10
ЖурналInternational Journal of Mechanics
Том14
СостояниеОпубликовано - 1 янв 2020

Предметные области Scopus

  • Физика и астрономия (все)
  • Электротехника и электроника

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