Implementing Runge-Kutta Method of Sixth-Order for Numerical Solution of Fuzzy Differential Equations

The article talks about the increasing importance of the practical use of fuzzy differential equations in modeling complex problems in various fields, such as science and engineering, as these differential equations allow for obtaining accurate results for systems that suffer from uncertainty or incomplete knowledge. Fuzzy differential equations are a suitable alternative to ordinary differential equations if nullity and ambiguity are present in the problem. The article presents a new method for solving fuzzy differential equations using Seikkala derivative techniques, which is based on the numerical approach used in Sixth's Rang-Kutta method. A comprehensive analysis of errors is presented, and the method is applied to solve some linear and nonlinear Cauchy problems using MATLAB program to obtain accurate numerical results close to the exact solution. The article hopes that it will help enhance the reader's understanding of these modern techniques in solving fuzzy differential equations, and improve the ability to apply them in practical solutions.