Multistep Collocation Methods for Volterra Integral Equations with Weakly Singular Kernels
Year: 2019
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 1 : pp. 67–86
Abstract
A multistep collocation method on uniform grids for weakly singular Volterra integral equations is considered. The initial integral equation is modified by a smoothing transformation and then solved by a multistep collocation method on a uniform grid. Convergence and linear stability are also studied. Numerical results demonstrate the efficiency of the method.
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/eajam.030118.070518
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 1 : pp. 67–86
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Multistep collocation method Volterra integral equation weakly singular kernel.
-
A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent
Ma, Zheng | Stynes, MartinJournal of Computational and Applied Mathematics, Vol. 454 (2025), Iss. P.116164
https://doi.org/10.1016/j.cam.2024.116164 [Citations: 0] -
Barycentric rational collocation methods for Volterra integral equations with weakly singular kernels
Li, Min | Huang, Chengming | Ming, WanyuanComputational and Applied Mathematics, Vol. 38 (2019), Iss. 3
https://doi.org/10.1007/s40314-019-0890-9 [Citations: 6] -
Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent
Ma, Zheng | Stynes, MartinJournal of Scientific Computing, Vol. 100 (2024), Iss. 2
https://doi.org/10.1007/s10915-024-02593-3 [Citations: 2] -
Highly stable multistep Runge–Kutta methods for Volterra integral equations
Wen, Jiao | Xiao, Aiguo | Huang, ChengmingComputational and Applied Mathematics, Vol. 39 (2020), Iss. 4
https://doi.org/10.1007/s40314-020-01351-z [Citations: 4] -
Two postprocessing techniques for barycentric rational collocation methods applied to weakly singular VIEs
Zhao, Zexiong | Huang, ChengmingNumerical Algorithms, Vol. (2024), Iss.
https://doi.org/10.1007/s11075-024-01992-9 [Citations: 0] -
Solve Riemann–Liouville boundary value problems using collocation boundary value methods with the graded mesh
Chen, Liang | Ma, JunjieJournal of Computational and Applied Mathematics, Vol. 443 (2024), Iss. P.115762
https://doi.org/10.1016/j.cam.2024.115762 [Citations: 1]