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Volume 12, Issue 4
Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations

Jingjun Zhao, Teng Long & Yang Xu

DOI: 10.4208/nmtma.OA-2018-0084

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1039-1065.

Published online: 2019-06

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  • 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.

  • Keywords

Collocation method, Volterra integral equation, weakly singular kernel, convergence.

  • AMS Subject Headings

65L20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hit_zjj@hit.edu.cn (Jingjun Zhao)

yangx@hit.edu.cn (Yang Xu)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-12-1039, author = {Zhao , JingjunLong , Teng and Xu , Yang}, title = {Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0084}, url = {http://global-sci.org/intro/article_detail/nmtma/13214.html} }
TY - JOUR T1 - Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations AU - Zhao , Jingjun AU - Long , Teng AU - Xu , Yang JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1039 EP - 1065 PY - 2019 DA - 2019/06 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0084 UR - https://global-sci.org/intro/article_detail/nmtma/13214.html KW - Collocation method, Volterra integral equation, weakly singular kernel, convergence. AB -

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.

Zhao , JingjunLong , Teng and Xu , Yang. (2019). Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations. Numerical Mathematics: Theory, Methods and Applications. 12 (4). 1039-1065. doi:10.4208/nmtma.OA-2018-0084
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