Analytical and computational methods for a class of nonlinear singular integral equations

Sonia Seyed Allaei, Teresa Diogo, Magda Rebelo

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider a class of nonlinear singular Hammerstein Volterra integral equations. In general, these equations will have kernels containing both an end point and an Abel-type singularity, with exact solutions being typically nonsmooth. Under certain conditions, a uniformly convergent iterative solution is obtained on a small interval near the origin. In this work, two product integration methods are proposed and analyzed where the integral over a small initial interval is calculated analytically, allowing the optimal convergence rates to be achieved. This is illustrated by some numerical examples.

Original languageEnglish
Pages (from-to)2-17
Number of pages16
JournalApplied Numerical Mathematics
Volume114
Issue numberSI
DOIs
Publication statusPublished - Apr 2017

Keywords

  • Hammerstein equations
  • Iterative solution
  • Nonlinear Volterra integral equation
  • Product integration method
  • Weakly singular kernel

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