Affiliations: [a] Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
| [b] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Correspondence:
[*]
Corresponding author. Mohammad Ali Fariborzi Araghi, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Zip code 14676-86831, Tehran, Iran Fax: +98 2188385777. E-mails: m_fariborzi@iauctb.ac.ir and fariborzi.araghi@gmail.com.
Abstract: In this paper, by using the fuzzy CESTAC method and the CADNA library a procedure is proposed to control the step size for solving the fuzzy differential equation with fuzzy boundary conditions based on the finite differences method under generalized H-differentiability (gH-differentiability). An algorithm is presented to implement the discrete stochastic arithmetic for solving the given fuzzy boundary value problem on the C++ code via the CADNA library. Also, a theorem is proved to show the accuracy of results based on the concept of the common proximity of two fuzzy numbers. Finally, some examples are solved by using the proposed algorithm to illustrate the effectiveness of applying the stochastic arithmetic (SA) in place of the floating-point arithmetic (FPA) to validate the results and find the optimal solution.
Keywords: Finite differences method, Fuzzy boundary value problem (FBVP), Stochastic arithmetic, CESTAC method, CADNA Library
