Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5

Abstract

The article exposes the use of the Runge-Kutta Fehlberg method of order five, a rarely studied methodology, to address the complexity involved in solving fuzzy hybrid differential equations. The study focuses on evaluating the reliability and accuracy of this method in contrast to recognized procedures, providing a thorough analysis of its performance. The article assesses the effectiveness of the RK-Fehlberg scheme by comparing its results with exact solutions, using thorough analysis and well-supported examples. This comparison analysis highlights the potential of the method to provide more accuracy compared to classic methods like Euler, improved, or modified schemes. The article demonstrates the strength and effectiveness of the method by using numerical examples. This not only helps improve computational techniques for solving fuzzy hybrid systems but also highlights the wide range of applications and reliability of the Runge–Kutta Fehlberg method in mathematical modeling and analysis.

Keywords

• Hybrid differential equations
• fuzzy differential equations
• numerical solutions
• runge-kutta method
• runge-kutta fehlberg method
• 00A05