An Improved Fifth-Order Runge-Kutta Method with Higher Accuracy and Efficiency for Solving Initial Value Problems

Habibah, Ummu
Medrano, Fermin Franco
Permana, Adith Chandra
Ardiana, Dita
Trisilowati

Science and Technology Indonesia
Vol. 10 No. 3 (2025): July

Solving initial value problems (IVPs) in ordinary differential equations (ODEs) often requires numerical methods, with the fifth-order Runge-Kutta method being a widely used approach due to its balance between accuracy and computational efficiency. A novel and straight forward formula for the fifth order Runge-Kutta method is proposed, aiming to simplify calculations while maintaining high accuracy and stability. The method is derived using an optimized Taylor series expansion, leading to a more efficient formulation. Numerical experiments are conducted to compare the proposed method with existing fifth-order Runge-Kutta methods. The results showthat the proposed formula out performs existing methods in terms of accuracy, stability, and computational efficiency. This new formula provides a practical alternative for solving IVPs in ODEs with improved performance.