“…The most popular integral equations are the Fredhom integral equations and the Volterra integral equations. The Fredholm integral equation can be considered as a reformulation of the elliptic partial differential equation and the Volterra integral equation is a reformulation of the fractional-order differential equation, which has wide applications in modeling the real problems, for instance, the chaotic system [ 4 ], the dynamics of COVID-19 [ 5 ], the motion of beam on nanowire [ 6 ], the capacitor microphone dynamical system [ 7 ], etc. Since these integral equations usually can not be solved explicitly, numerical methods are necessary to be considered.…”