ABSTRACT
The finite difference grid for the general implicit Adams-Moulton FDEs is illustrated in Figure 7.21. The general formula for the implicit Adams-Moulton FDEs is:
_ dy = h [Pk(S)]Il+1 ds y" -I
(7.251 )
where k denotes the order of the Newton backward-difference polynomial fit at base point n + 1. Integrating Eg. (7.251), evaluating the results for the limits of integration, introducing the expressions for the appropriate backward differences at point n + I, and simplifying the result yields the general implicit Adams-Moulton FDE:
YIl+l = Yll + j3h(al 1n+1 + aoln + a_I In-I + ...) O(h"), a At ::: C (7.252)
where the coefficients j3 and ai (i = I, 0, -1, ...), the global order n, and the stability limit, a At ::: C, are presented in Table 7.12.
