This thesis presents the work in applying the Pasic method for solving ordinary differential equations to the Ideal Adiabatic Stirling model. The model is presented along with the formulation of the coupled first order differential equations. Also, the Pasic method is presented along with some of the foundational numerical methods, which the method is based upon. A "C" program was written to solve the Ideal Adiabatic model utilizing the Pasic method. An explanation of the logic is given. The Pasic method is shown to solve the Ideal Adiabatic model and the results are presented. Two areas of concern are the solve time of the CPU and the error associated with the heat in the regenerator - it should be zero over a cycle. A minimum time of 0.2 and 0.35 seconds solves, respectively, the Ford-Philips 4-215 engine and Ross-90 engine with four sub-domains. Even with the large sub-domains the error of Q ris under 1%. The Pasic method is 12 and 7.6 times faster respectively for the Ross-90 and Ford-Philips 4-215 engine as compared to the Runge-Kutta method. One reason for the improved speed is the logic of the program where the energy differentials are solved atter the temperature differentials, thereby eliminating the fixed-point iterations. Further comparison of the Pasic method with the Runge-Kutta method may be warranted. The future research possibilities are significant: the Pasic method as presented deserves further research; the Advanced Pasic method needs to be applied to Stifling analysis; and the Pasic method applied to partial differential equations deserves investigation.