Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations

In the current study, an efficient iterative scheme which is based on the two powerful tools called the quasilinearization method and the Jacobi-Galerkin method is proposed to solve a type of functional Volterra integral equations. According to the iterative structure of the proposed method, an error analysis of the method is provided. This method can overcome the difficulty of solving nonlinear system of algebraic equations associated with the Galerkin method in treating nonlinear functional Volterra integral equations directly. Moreover, under sufficient conditions, the suggested method has spectral accuracy. In the end, several numerical experiments are reported to confirm the efficiency and accuracy of the proposed scheme. •A family of strong nonlinear functional Volterra integral equations investigated.•The method is a combination of the quasilinearization and the Galerkin methods.•The convergence analysis of the numerical method is studied in details.•Applicability and accuracy of the method are checked on some examples.