TY - JOUR

T1 - Spline collocation for Volterra integral equations with improved accuracy

AU - Макаров, Антон Александрович

AU - Куликов, Егор Константинович

PY - 2026/5/15

Y1 - 2026/5/15

N2 - We propose a new spline collocation-based approach for solving Volterra integral equations of the first and second kinds. The solution is represented as a linear combination of quadratic minimal splines of maximal smoothness, with the coefficients determined through specialized local approximation schemes (quasi-interpolation). Numerical experiments demonstrate that the use of non-polynomial splines leads to higher accuracy of the approximate solution compared to previously proposed approaches based on -splines, including approaches defined on nonuniform grids.

AB - We propose a new spline collocation-based approach for solving Volterra integral equations of the first and second kinds. The solution is represented as a linear combination of quadratic minimal splines of maximal smoothness, with the coefficients determined through specialized local approximation schemes (quasi-interpolation). Numerical experiments demonstrate that the use of non-polynomial splines leads to higher accuracy of the approximate solution compared to previously proposed approaches based on -splines, including approaches defined on nonuniform grids.

KW - Local approximation

KW - Minimal splines

KW - Quasi-interpolation

KW - Spline collocation method

KW - Volterra integral equations

UR - https://www.mendeley.com/catalogue/ee0b3b9a-836c-3e2e-ae68-9d3b018f1a7b/

U2 - 10.1007/s11075-026-02388-7

DO - 10.1007/s11075-026-02388-7

M3 - Article

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

ER -