Single step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation

Adam–Bashforth method and Adam–Moulton method are two known multi-step methods for finding the numerical solution of the initial value problem of ordinary differential equation. These two methods used the Newton backward difference method to approximate the value of f(x,y)f(x,y) in the integral equation which is equivalent to the given differential equation.