An explicit numerical integration method is further developed. The method is based on the relationship that m-step Adams-Moulton method is linear convex combination of the
-step Adams-Moulton and m-step Adams-Bashforth method with a fixed weighting coefficients. A general form is used to evaluate the recurrence expressions using the different number of previous mesh points. The analytical upper bound of modified predictor-corrector method is given in the closed form. The expressed order of convergence is now
The explicit numerical algorithm is given for modified 3-step predictor-corrector method. Some numerical examples, for the different kind of problems, first- and second-order nonlinear initial value problems, are used to demonstrate the efficiency and the accuracy of the proposed numerical method. The calculated numerical solutions show superiority of presented modified predictor-corrector method to the standard Adams-Bashforth-Moulton predictor-corrector method.
