Continuous Local Splines of the Fourth Order of Approximation and Boundary Value Problem

doi:10.46300/9106.2020.14.59

International Journal of Circuits, Systems and Signal Processing

2020

DOI: 10.46300/9106.2020.14.59

|View full text |Cite

Continuous Local Splines of the Fourth Order of Approximation and Boundary Value Problem

Abstract: This paper discusses the construction of polynomialand non-polynomial splines of the fourth order of approximation.The behavior of the Lebesgue constants for the left, the right, andthe middle continuous cubic polynomial splines are considered.The non-polynomial splines are used for the construction of thespecial central difference approximation. The approximation offunctions, and the solving of the boundary problem with thepolynomial and non-polynomial splines are discussed. Numericalexamples are done.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2021

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 10 publications

(15 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Application of Non-polynomial Splines to Solving Differential Equations

Бурова

2020

Wseas Transactions on Mathematics

View full text Add to dashboard Cite

The application of the local polynomial and non-polynomial to the construction of methods for numerically solving the heat conduction problem is discussed. The non-polynomial splines are used here to approximate the partial derivatives. Formulas for numerical differentiation based on the application of the nonpolynomial splines of the fourth order of approximation are constructed. Particular attention is paid to polynomial, trigonometric, exponential, polynomial-trigonometric and polynomial-exponential splines. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference scheme. New approximations with splines of the Lagrange and Hermite type with new properties are obtained. These approximations take into account the first and second derivatives of the function being approximated. Numerical examples are given.

show abstract

Application of Non-polynomial Splines to Solving Differential Equations

Бурова

2020

Wseas Transactions on Mathematics

View full text Add to dashboard Cite

show abstract

Approximation on Manifold

Dem’yanovich

2021

Wseas Transactions on Mathematics

View full text Add to dashboard Cite

The purpose of this work is to obtain an effective evaluation of the speed of convergence for multidimensional approximations of the functions define on the differential manifold. Two approaches to approximation of functions, which are given on the manifold, are considered. The firs approach is the direct use of the approximation relations for the discussed manifold. The second approach is related to using the atlas of the manifold to utilise a well-designed approximation apparatus on the plane (finit element approximation, etc.). The firs approach is characterized by the independent construction and direct solution of the approximation relations. In this case the approximation relations are considered as a system of linear algebraic equations (with respect to the unknowns basic functions ωj (ζ)). This approach is called direct approximation construction. In the second approach, an approximation on a manifold is induced by the approximations in tangent spaces, for example, the Courant or the Zlamal or the Argyris fla approximations. Here we discuss the Courant fla approximations. In complex cases (in the multidimensional case or for increased requirements of smoothness) the second approach is more convenient. Both approaches require no processes cutting the manifold into a finit number of parts and then gluing the approximations obtained on each of the mentioned parts. This paper contains two examples of Courant type approximations. These approximations illustrate the both approaches mentioned above.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Continuous Local Splines of the Fourth Order of Approximation and Boundary Value Problem

Cited by 2 publications

References 10 publications

Application of Non-polynomial Splines to Solving Differential Equations

Application of Non-polynomial Splines to Solving Differential Equations

Approximation on Manifold

Contact Info

Product

Resources

About