Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind-Reference-Cited by-同舟云学术

Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind

Published:2023-11-16 Issue: Volume:23 Page:1-15
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
Short-container-title:

Author:

Burova I. G.¹,Alcybeev G. O.¹,Schiptcova S. A.¹

Affiliation:

1. The Department of Computational Mathematics, St. Petersburg State University, 7-9 Universitetskaya Embankment, St.Petersburg, RUSSIA

Abstract

This work is a continuation of a series of works on the use of continuous local polynomial splines for solving interpolation problems and for solving the Fredholm integral equation of the second kind. Here the construction of a numerical solution to the Fredholm integral equation of the second kind using local spline approximations of the second order and the seventh order of approximation is considered. This paper is devoted to the investigation of the stability of the solution of the integral equation using these local splines. Approximation constants are given in the theorem about the error of approximation by the considered splines. Numerical examples of the application of spline approximations of the second and seventh order of approximation for solving integral equations are given.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Reference24 articles.

1. V.R. Ibrahimov, G.Y.U. Mehdiyeva, X.G. Yue, M.K.A. Kaabar, S. Noeiaghdam, D.A. Juraev, Novel Symmetric Numerical Methods for Solving Symmetric Mathematical Problems, International Journal of Circuits, Systems and Signal Processing, Vol.15, 2021, pp. 1545-1557.

2. A. Carpio, E. Cebrian, Positivity Preserving High Order Schemes for Angiogenesis Models, International Journal of Nonlinear Sciences and Numerical Simulation, 2021, DOI: 10.1515/ijnsns-2021-0112.

3. P.Assari, F.Asadi-Mehregan, The Approximate Solution of Charged Particle Motion Equations in Oscillating Magnetic Fields using the Local Multiquadrics Collocation Method, Engineering with Computers, Vol.37, No. 1, 2021, pp. 21-38. DOI: 10.1007/s00366-019-00807-z.

4. S. Saha, V. Kumar, A. N. Das, An Elastic Half Space with a Moving Punch, WSEAS Transactions on Applied and Theoretical Mechanics, Vol. 16, 2021, pp. 245-249.

5. L. Hącia, K. Bednarek, A. Tomczewski, Computational Results for Integral Modeling in Some Problems of Electrical Engineering, WSEAS International Conference on Computers, 2007, pp. 114-119.