Abstract: We present a framework for the stability analysis of a linearized semi-implicit Runge-Kutta Method. To determine an A or L stable LSIRM. The conventional procedure has been to estimate the parameters from the construction and then test for A-or L-stability. It is now questioned whether conditions cannot be imposed on the parameters a priori to achieve the required stability. The general LSIRM of order two and three respectively were, therefore, constructed using Taylor’s expansion. The stability function for each method was derived from the stability analysis; criteria were set for A-or L-stability.