Abstract: Adams-Moulton methods for k = 2 and k = 3 were constructed together with their continuous forms using multi-step collocation methods. The continuous forms were then evaluated at various grid points to produce the block Adams-Moulton methods.

The block methods were then reformulated as a sub-class of two step Runge-Kutta methods (TSRK). Both the Adams and the reformulated methods were applied to solve initial value problems and the reformulated methods proved superior in terms of stability.

Keywords: Reformulation, Adams-Moulton, block method, two-step, Runge-Kutta and collocation.