Numerical Solution of N th - Order Fuzzy Initial Value Problems by Fourth Order Runge-Kutta Method Basesd On Centroidal Mean

Abstract

In this paper, a numerical method for N th - order fuzzy initial value problems (FIVP) based on Seikkala derivative of fuzzy process is studied. The fourth order Runge-Kutta method based on Centroidal Mean (RKCeM4) is used to find the numerical solution and the convergence and stability of the method is proved. This method is illustrated by solving second and third order FIVPs. The results show that the proposed method suits well to find the numerical solution of N th - order FIVPs. Keywords - Fuzzy numbers, N th - order Fuzzy Initial Value Problems, Runge-Kutta method, Centroidal Mean, Lipschitz condition.