A comparative study of 4th-order and 6th-stage 5th-order Runge-Kutta methods for solving autonomous differential equations

In this study, we utilized the Sixth-Stage Fifth-Order Runge-Kutta method and the Fourth-Order Runge-Kutta (RK4) method to address First-Order Autonomous Differential Equations with Initial Value Problems (IVPs). Both methods demonstrate considerable efficacy and are well-suited for resolving challenges encountered in engineering and scientific contexts. To evaluate the accuracy of the numerical solutions obtained, we compared the approximate results with exact solutions, revealing a strong correlation between the two. Additionally, we analyzed the error terms associated with both methods and provided a comparative evaluation using a relevant example.