Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
Document Type
Article
Publication Date
1-1-2018
Abstract
In this paper, an extended fourth-order Runge–Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f′, instead of using the evaluations of f only. The proposed extended Runge–Kutta method and its error analysis, which guarantees pointwise convergence, are given in detail. Furthermore, the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments.
Keywords
Fuzzy ordinary differential equations, Fuzzy differentiability, Characterization theorem, Error analysis, Runge–Kutta methods
Publication Title
Fuzzy Sets and Systems
Divisions
fsktm
Funders
University of Malaya HIR under Grant UM.C/625/HIR/MOHE/FCSIT/08, B000008
Volume
331
Publisher
Elsevier