A-stable Two Derivative Mono-Implicit Runge-Kutta Methods for ODEs

An A-stable Two Derivative Mono Implicit Runge-Kutta (ATDMIRK) method is considered herein for the numerical solution of initial value problems (IVPs) in ordinary differential equation (ODEs). The methods are of high-order A-stable for p=q= 2s+1 ₛ₌₂⁷\ The p, q and s are the order of the input, output and the stages of the methods respectively. The numerical results affirm the superior accuracy of the newly develop methods compare to the existing ones.