The 8th-order Adams-Bashforth-Moulton method is a predictor-corrector numerical integration method. It can solve differential equations of the form \(y’=f(t_k,y_k)\) with two steps. Each step in the ADM8 algorithm consists of an Adams-Bashforth predictor step and an Adams-Moulton corrector step. This method solves differential equations of this generalized form
$$y_{k+1}=\Sigma^p_{i=1}\alpha_iy_{k+1-i}+h\Sigma^p_{i=0}\beta_iy'{k+1-i}+E$$
with \(E\) being the error term. When $latex\beta_0=0$ then this is the explicit Adams-Bashforth method. When \(\beta_0\neq0\) then it is the Adams-Moulton implicit corrector equation.
The predictor equation is
$$P{k+1}=\Sigma^8_{i=1}\alpha_iy_{k+1-i}+h\Sigma^8_{i=0}\beta_iy'{k+1-i}+E_p$$
And the corrector equation is
$$C{k+1}=\Sigma^7_{i=1}\alpha_iy_{k+1-i}+h\Sigma^7_{i=0}\beta_iy’_{k+1-i}+E_p$$
NumericalSolutionPoint2020