Error Analysis and Accuracy Assessment of Runge-Kutta's Method in Solving Ordinary Differential Equations

The primary focus of this paper is the presentation of Runge-Kutta's method as a method for addressing initial value problems (IVP) in ordinary differential equations (ODE). This method demonstrates practical efficiency and suitability for addressing these problems. To ensure accuracy, we perform comparisons between numerical solutions and exact solutions. The numerical solutions are in good agreement with the exact solutions. To obtain greater solution accuracy the step size must be reduced to extremely small values. Our investigation reaches its terminus as we examine and calculate the discrepancies in Runge-Kutta's method across various step sizes.