Fuzzy Form of Euler Method to Solve Fuzzy Differential Equations

Abstract

Background: The Euler method is a elementary method to solve fuzzy differential equations numerically. Several authors have explored the Euler method by applying various approaches and derivative concepts. Methods: This paper proposes a fuzzy form of the Euler method to solve fuzzy initial value problems. Novelty of this approach is that the method developed based on fuzzy arithmetic. The solution by this method is readily available in the form of fuzzy-valued function. The method does not require to re-write fuzzy differential equation into a system of two crisp ordinary differential equations. Results: The algorithm of proposed method and local error expression are discussed. An illustration and solution of the fuzzy Riccati equation are provided for the applicability of the method. Conclusion: The proposed Euler method is a natural generalization of crisp Euler method. It is very efficient in solving linear and nonlinear fuzzy differential equations. One of the advantage of this method is that the solution obtained by the method is always a fuzzy-valued function due to well-defined fuzzy arithmetic.