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Adams-Bashforth-Moulton Method

The methods of Euler, Heun, Taylor and Runge-Kutta are called single-step methods because they use only the information from one previous point to compute the successive point, that is, only the initial point is used to compute and in general is needed to compute . After several points have been found it is feasible to use several prior points in the calculation. The Adams-Bashforth-Moulton method uses in the calculation of . This method is not self-starting; four initial points , , , and must be given in advance in order to generate the points . A desirable feature of a multistep method is that the local truncation error (L. T. E.) can be determined and a correction term can be included, which improves the accuracy of the answer at each step. Also, it is possible to determine if the step size is small enough to obtain an accurate value for , yet large enough so that unnecessary and time-consuming calculations are eliminated. If the code for the subroutine is f