Convergence of numerical methods for fuzzy differential equations

Article type: Research Article

Authors: Cheng, Yan | You, Cuilian^{; *}

Affiliations: College of Mathematics and Information Science, Hebei University, China

Correspondence: [*] Corresponding author. Cuilian You, College of Mathematics and Information Science, Hebei University, Baoding 071002, China. E-mail: yycclian@163.com.

Abstract: In this paper, semi-implicit and implicit Euler schemes for homogeneous fuzzy differential equations with perturbation term reflected by Liu process are introduced. As to the application with implicit term in numerical scheme, we must make the result gradually explicit by iterative method. In order to obtain numerical method with higher accuracy than fuzzy Euler method, fuzzy trapezoidal scheme is derived. Fuzzy trapezoidal scheme is an implicit formation, which is complicated and cumbersome in computational processing. For the sake of this problem, fuzzy Euler-trapezoidal method is proposed to simplify the algorithm. Furthermore, the convergence properties are investigated for numerical methods. At last, local convergence is proved better than global convergence.

Keywords: Credibility, fuzzy differential equations, Liu process, numerical methods, convergence

DOI: 10.3233/JIFS-191856

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 4, pp. 5257-5266, 2020