Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations

Authors

  • Jingjun Zhao Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China.
  • Teng Long Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China.
  • Yang Xu Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China.

DOI:

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

Keywords:

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

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.

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Published

2019-10-12

Issue

Vol. 12 No. 4 (2019)

Section

Articles