Linear k-Step Methods for Solving Nth-order Fuzzy Differential Equations

In this paper a particular numerical algorithm of linear k-step methods for solving initial value problem of N th-order fuzzy differential equations is presented. First of all we will transform an initial value problem of N th-order fuzzy differential equations to an initial value problem of first-order systems of fuzzy differential equations, then we solve this system, numerically. After that we obtain the approximate solution of the initial value problem of N th-order fuzzy differential equation. Also we will prove that the algorithm converges to the exact solution as the stepsize goes to zero and at the end the validity of the algorithm is illustrated by solving some examples.