A Comparative Analysis of Numerical Techniques: Euler-Maclaurin vs. Runge-Kutta Methods

This study introduces a novel higher-order implicit correction method derived from the Euler-Maclaurin formula to enhance the approximation of initial value problems. The proposed method surpasses the Runge-Kutta approach in accuracy, stability, and convergence. An error bound is established to demonstrate its theoretical reliability. To validate its effectiveness, numerical experiments are conducted, showcasing its superior performance compared to conventional methods. The results consistently confirm that the proposed method outperforms the Runge-Kutta method across various practical applications.