Numerical solution of nonlinear third-kind Volterra integral equations using an iterative collocation method

Abstract

In this paper, we discuss the application of an iterative collocation method based on the use of Lagrange polynomials for the numerical solution of a class of nonlinear third-kind Volterra integral equations. The approximate solution is given by explicit formulas. The error analysis of the proposed numerical method is studied theoretically. Some numerical examples are given to confirm our theoretical results.

Keywords:

• Nonlinear third-kind Volterra integral equation
• Collocation method
• Iterative method
• Lagrange polynomials
• Convergence analysis

Mathematics Subject Classifications:

• 45E99
• 45G05
• 65R20

Acknowledgments

The third author (P. Lima) acknowledges financial support from FCT, through projects UIDB/04621/2020, UIDP/04621/2020.

Disclosure statement

No potential conflict of interest was reported by the author(s).