In this paper we discuss the four-stage index-2 singly diagonally implicitRunge-Kutta method, which is used to solve stiff ordinary differential equations (SODE). Stiff problemsrequire a method where step size is not restricted by the method's stability. We desire SDIRK to be Astablethat has no stability restrictions when solving y= ly with Rel and, so by choosing suitablestability function we can determine appropriate constant (g) to formulate SDIRK integrator to solve SODE. We select the second stage of the internal stage as embedded method to perform low orderestimate for error predictor. The strategy for choosing the step size is adopted from the strategy proposedby Hall(1996:6). And the algorithm that is developed in this paper is implemented using MATLAB 5.3, which is running on Windows95 environment. Our performance measurement’s local truncation erroraccuracy, and efficiency were evaluated by statistical results of sum of steps, sum of calling functions,average of Newton iterations and elapsed times. As the results, our numerical experiment show thatSDIRK is unconditionally stable. By using Hall's step size strategy, the method can be implemente defficiently, provided that suitable parameters are used.Alhadi B. dan T. Basaruddin; Jurusan Matematika, FMIPA–Universitas Indonesia Fakultas Ilmu Komputer– Universitas Indonesia
