High order SDIMSIMs

In this paper, we construct a new class of second derivative diagonally implicit multistage integration methods (SDIMSIMs) with Runge–Kutta stability property and A-stability. In this construction p = q = 2s and r = s, where p is the order, q is the stage order, r is the number of external stages, and s is the number of internal stages of the method. Efficiency of the constructed method is shown by numerical experiment.