Ummu Habibah, Fermin Franco Medrano, Adith Chandra Permana, Dita Ardiana, Trisilowati
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 straightforward 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 show that the proposed formula outperforms 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. © 2025, Magister Program of Material Sciences, Graduate School of Sriwijaya University. All rights reserved.
Department of Mathematics, Brawijaya University, East Java, 65145, Indonesia; Department of Mathematics, Faculty of Science, Autonomous University of Baja California, 21100, Mexico
