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

AbstractIn 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 equationCollocation methodIterative methodLagrange polynomialsConvergence analysis.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe third author (P. Lima) acknowledges financial support from FCT, through projects UIDB/04621/2020, UIDP/04621/2020.