Solving Implicit Equations Arising from Adams-Moulton Methods

A new algorithm is given in this paper, which uses functional iteration to solve the implicit equations generated by the Adams-Moulton method. Compared with traditional function iteration, it has three advantages: (1) the center of the circle of convergence for the iteration moves to the left in h plane; (2) the radius of the circle is much enlarged; (3) for a fixed number of iterations, in practice, we can view it as an explicit method since it has a very large absolute stability region. The method is very suitable for stiff system, especially for very large systems.