High Order Stable Methods Derived from the Composition of Reverse Adams Moulton and Adams Moulton Methods

In this work, a family of high order stable methods is derived for the solution of stiff ordinary differential equation. The derivation is done by pairing Reverse Adams Moulton (RAM) and Adams Moulton (AM) methods and applying shift-operator E on them. The resultant one-block methods are A-Stable for order ten and -stable with for order eleven. The methods are tested on some stiff initial value problems to showcase the effectiveness.