TY - JOUR

T1 - The Application of Local Splines in a Numerical Solution of Functional Equations

AU - Бурова, Ирина Герасимовна

AU - Пацукевич, Екатерина Александровна

PY - 2026/4/16

Y1 - 2026/4/16

N2 - The authors considered the construction and application of continuous polynomial and nonpolynomial local spline approximations to solving integral and differential equations. A distinctive feature of constructing these spline approximations is that the approximations do not require solving systems of equations. An approximation of a function on a grid interval is constructed as the sum of products of basis splines and the function values at the grid nodes. To construct basis splines, we use approximation relations. This paper continues research on constructing splines of this type and applying them to solving integral equations and to differential equations (the Cauchy problem). We discuss the application of continuous polynomial splines of a maximum defect in solving functional equations, solving Fredholm integral equations of the second kind, constructing quadrature formulas, solutions to the Cauchy problem, the stability of a solution to the Cauchy problem. The solution was constructed using local splines. The paper presents the results of numerical experiments.

AB - The authors considered the construction and application of continuous polynomial and nonpolynomial local spline approximations to solving integral and differential equations. A distinctive feature of constructing these spline approximations is that the approximations do not require solving systems of equations. An approximation of a function on a grid interval is constructed as the sum of products of basis splines and the function values at the grid nodes. To construct basis splines, we use approximation relations. This paper continues research on constructing splines of this type and applying them to solving integral equations and to differential equations (the Cauchy problem). We discuss the application of continuous polynomial splines of a maximum defect in solving functional equations, solving Fredholm integral equations of the second kind, constructing quadrature formulas, solutions to the Cauchy problem, the stability of a solution to the Cauchy problem. The solution was constructed using local splines. The paper presents the results of numerical experiments.

KW - Cauchy problem

KW - Fredholm integral equations

KW - differential equations with delay

KW - functional equations

KW - integral equations

KW - maximum defect

KW - splines

UR - https://www.mendeley.com/catalogue/a6f30426-7e20-3dae-9606-8a730a84f0ee/

U2 - 10.37394/23201.2026.25.5

DO - 10.37394/23201.2026.25.5

M3 - Article

VL - 25

SP - 43

EP - 60

JO - WSEAS Transactions on Circuits and Systems

JF - WSEAS Transactions on Circuits and Systems

SN - 1109-2734

ER -