Solving the Linear Arms Race Model Using SAWI Transformation

Abstract

This research explores the application of SAWI transformation to solve the arms race model, offering an analytical alternative to traditional numerical methods. such as the Runge-Kutta algorithm. By converting complex systems of linear first-order ordinary differential equations into simpler algebraic forms, the SAWI method enables the derivation of exact, closed-form analytical solutions that describe how nations and armament levels evolve. Numerical simulations in MATLAB further validate the method’s computational precision, highlighting how factors such as reaction coefficients and economic fatigue determine whether a system leads to a runaway arms race or a stable balance of power. While the study demonstrates that the SAWI transformation effectively reduces numerical approximation errors for linear systems, it also notes the need for future improvements to handle more complex nonlinear dynamics found in real-world international relations.