A combination method to solve the system of nonlinear Volterra integral equations

In this paper, an efficient combination approach based on quasilinearization and spectral collocation methods is proposed for solving a system of nonlinear Volterra integral equations of the second kind. Throughout this process, the nonlinear system is turned into a sequence of the linear systems and solved using Legendre spectral collocation method. An illustrative example is provided to verify the efficiency and accuracy of the method.