Quasilinearization-based Legendre collocation method for solving a class of functional Volterra integral equations

Abstract

In this paper, a combination of the quasilinearization and the Legendre spectral collocation methods is introduced to approximate the solution of the nonlinear functional Volterra integral equations. Throughout this process, the quasilinearization method converts the nonlinear functional Volterra integral equation to a sequence of linear integral equations. Then, in each iteration, the obtained linear integral equation is solved using the Legendre spectral collocation method. After that, a convergence analysis is discussed in detail. Finally, several numerical examples are included to demonstrate the capability and validity of the proposed method.