Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations

D. Nazari Susahab; S. Shahmorad

Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations

Numerical Analysis 2014-12-17 v3

Authors: D. Nazari Susahab , S. Shahmorad

Abstract

We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-\tau)^{\alpha-1}$ with $0 <\alpha <1.$ Convergence orders of the methods are determined and their superconvergence is also analyzed. The paper closes with numerical examples and application to fractional differential equations.

Keywords

volterra equations differential equations numerical analysis

Cite

@article{arxiv.1408.4029,
  title  = {Multistep collocation methods for weakly singular Volterra integral equations with application to fractional differential equations},
  author = {D. Nazari Susahab and S. Shahmorad},
  journal= {arXiv preprint arXiv:1408.4029},
  year   = {2014}
}

Comments

This paper has been withdrawn by the author due to finding some errors

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