WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Application of Local Splines for Solving Integral Equations of Several Variables
Authors: , ,
Search Articles
Abstract: The proposed approximation of a function of several variables is based on the direct product of local splines of one variable. The approximation is built on each elementary parallelepiped separately and is reduced to calculating the sum of the products of the function values and the basis splines. The use of non-polynomial basis splines with different properties in different directions allows us to obtain a qualitatively better approximation. Solving the Fredholm integral equation of the second kind of several variables is reduced to calculating the integrals of the product of the kernel and the basis splines and solving a system of linear algebraic equations. A comparison of the results of the numerical solution of integral equations by the proposed method and the results of applying other methods is given.
Keywords:
Fredholm Integral equations of the second kind, Local splines, Nonpolynomial splines, Approximation, Interpolation, Several Variables
Pages: 147-157
DOI: 10.37394/23206.2026.25.14