Application of Splines of the Fifth Order Approximation for Solving Integral Equations of the Second Kind with a Weak Singularity

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Application of Splines of the Fifth Order Approximation for Solving Integral Equations of the Second Kind with a Weak Singularity. / Бурова, Ирина Герасимовна ; Алцыбеев, Глеб Олегович.

в: WSEAS Transactions on Systems, Том 24, 26.03.2025, стр. 66-74.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{12db509f5c3645dda7bef6db6d4eb13c,

title = "Application of Splines of the Fifth Order Approximation for Solving Integral Equations of the Second Kind with a Weak Singularity",

abstract = "Previously, the authors showed that local splines of the different order of approximation give good results on both uniform and non-uniform grids. In this paper, we investigate the stability of the numerical method based on the splines of the fifth order of approximation and the use of these splines for solving weak singular Fredholm and Volterra integral equations of the second kind. The solution method consists of replacing the unknown function under the integral sign with a spline approximation. We compare the errors of the solutions of integral equations obtained using splines of the second, fifth, and seventh orders with the results which were received in recent papers by using other methods. The results of the numerical experiments are presented in this paper.",

keywords = "Fredholm integral equation, Volterra integral equation, local basis splines, polynomial spline approximations, stability, weak singularity",

author = "Бурова, {Ирина Герасимовна} and Алцыбеев, {Глеб Олегович}",

year = "2025",

month = mar,

day = "26",

doi = "10.37394/23202.2025.24.8",

language = "English",

volume = "24",

pages = "66--74",

journal = "WSEAS Transactions on Systems",

issn = "1109-2777",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Application of Splines of the Fifth Order Approximation for Solving Integral Equations of the Second Kind with a Weak Singularity

AU - Бурова, Ирина Герасимовна

AU - Алцыбеев, Глеб Олегович

PY - 2025/3/26

Y1 - 2025/3/26

N2 - Previously, the authors showed that local splines of the different order of approximation give good results on both uniform and non-uniform grids. In this paper, we investigate the stability of the numerical method based on the splines of the fifth order of approximation and the use of these splines for solving weak singular Fredholm and Volterra integral equations of the second kind. The solution method consists of replacing the unknown function under the integral sign with a spline approximation. We compare the errors of the solutions of integral equations obtained using splines of the second, fifth, and seventh orders with the results which were received in recent papers by using other methods. The results of the numerical experiments are presented in this paper.

AB - Previously, the authors showed that local splines of the different order of approximation give good results on both uniform and non-uniform grids. In this paper, we investigate the stability of the numerical method based on the splines of the fifth order of approximation and the use of these splines for solving weak singular Fredholm and Volterra integral equations of the second kind. The solution method consists of replacing the unknown function under the integral sign with a spline approximation. We compare the errors of the solutions of integral equations obtained using splines of the second, fifth, and seventh orders with the results which were received in recent papers by using other methods. The results of the numerical experiments are presented in this paper.

KW - Fredholm integral equation

KW - Volterra integral equation

KW - local basis splines

KW - polynomial spline approximations

KW - stability

KW - weak singularity

UR - https://www.mendeley.com/catalogue/cf683a0e-832f-3945-8970-1c14aae159f2/

U2 - 10.37394/23202.2025.24.8

DO - 10.37394/23202.2025.24.8

M3 - Article

VL - 24

SP - 66

EP - 74

JO - WSEAS Transactions on Systems

JF - WSEAS Transactions on Systems

SN - 1109-2777

ER -

ID: 133623247