Boubaker polynomials collocation approach for solving systems of nonlinear Volterra–Fredholm integral equations

Abstract

Numerical schemes have been developed for solutions of systems of nonlinear mixed Volterra–Fredholm integral equations of the second kind based on the First Boubaker polynomials (FBPs). The classical operational matrices are derived. The unknown has been approximated by FBPs and the Newton–Cotes points were applied as the collocations points. Error estimate and convergence analysis of the proposed method have been proved. Some numerical experiments are considered. The results are compared with relevant studies in order to test the reliability, validity and effectiveness of the proposed approach.