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
Divisions
fsktm
Funders
University of Malaya HIR under Grant UM.C/625/HIR/MOHE/FCSIT/08, B000008
Publication Title
Fuzzy Sets and Systems
Volume
331
Publisher
Elsevier