Evolutionary techniques are used for the derivation of a six-stage sixth-order singly diagonally implicit Runge–Kutta–Nystrom (SDIRKN) method for the integration of second-order initial value problems (IVPs). This method is P-stable and is recommended for stiff and mildly stiff problems possessing an oscillatory solution. It also attains an order which is one higher than existing methods of this type. Thus, it outperforms the other existing methods of this type when applied to relevant systems of IVPs arising from the semi-disrcetization of partial differential equations (PDEs) with the method of lines (MoL).
Read full abstract