10.1007/s40096-021-00395-4

Product integration method for treating a nonlinear Volterra integral equation with a weakly singular kernel

  • Ahlem Nemer*1,
  • Zouhir Mokhtari1,
  • Hanane Kaboul1,
  1. Applied Mathematics Laboratory, University of Biskra, Biskra, 07000, DZ

Published in Issue 2021-04-08

How to Cite

Nemer, A., Mokhtari, Z., & Kaboul, H. (2021). Product integration method for treating a nonlinear Volterra integral equation with a weakly singular kernel. Mathematical Sciences, 16(1 (March 2022). https://doi.org/10.1007/s40096-021-00395-4
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Abstract

Abstract This work shed light on the solvability of a nonlinear Volterra integral equation in the case where the kernel of this equation is weakly singular. We certainly aim to get a precise solution. This can be achieved by applying a product integration method which is able to construct a nonlinear system. To solve the resulting system, it suffices to employ Broyden’s method. In the sequel, we add a computational application after the convergence proof of our approximate solution

Keywords

  • Broyden’s method,
  • Nonlinear system,
  • Volterra integral equation,
  • Product integration method

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