Close Search Advanced
Journals
Resources
About Us
Open Access

Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations

Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations
Preview
Add to basket

Year:    2019

Author:    Teng Long, Jingjun Zhao, Yang Xu, Teng Long, Yang Xu

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1039–1065

Abstract

In this paper, we consider super implicit multistep collocation methods for solving weakly singular Volterra integral equations. After the integral equations are regularized by smoothing transformations, super implicit multistep collocation methods are constructed. Convergence and the linear stability of these methods are analyzed. The theoretical result is also demonstrated by numerical examples.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0084

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 4 : pp. 1039–1065

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Collocation method Volterra integral equation weakly singular kernel convergence.

Author Details

Teng Long

Jingjun Zhao

Yang Xu

Teng Long

Yang Xu

  1. Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind

    Wang, Tongke | Lian, Huan | Ji, Lu

    Numerical Algorithms, Vol. 95 (2024), Iss. 4 P.1829

    https://doi.org/10.1007/s11075-023-01629-3 [Citations: 1]

  2. Generalized Multistep Collocation Methods for the First-Kind Volterra Integral Equations

    刘, 婧雅

    Operations Research and Fuzziology, Vol. 13 (2023), Iss. 03 P.1751

    https://doi.org/10.12677/ORF.2023.133175 [Citations: 0]

  3. Collocation boundary value methods for auto-convolution Volterra integral equations

    Liu, Ling | Ma, Junjie

    Applied Numerical Mathematics, Vol. 177 (2022), Iss. P.1

    https://doi.org/10.1016/j.apnum.2022.03.004 [Citations: 6]

  4. Highly stable multistep Runge–Kutta methods for Volterra integral equations

    Wen, Jiao | Xiao, Aiguo | Huang, Chengming

    Computational and Applied Mathematics, Vol. 39 (2020), Iss. 4

    https://doi.org/10.1007/s40314-020-01351-z [Citations: 3]

  5. Block collocation boundary value solutions of the first-kind Volterra integral equations

    Liu, Ling | Ma, Junjie

    Numerical Algorithms, Vol. 86 (2021), Iss. 2 P.911

    https://doi.org/10.1007/s11075-020-00917-6 [Citations: 7]