Fuzzy Volterra integro-differential equations using general linear method

• Main Authors: Abdul Majid, Zanariah, Rabiei, Faranak, Abd Hamid, Fatin Nadiah, Ismail, Fudziah
• Format: Article
• Language: English
• Published: MDPI 2019
• Online Access: http://psasir.upm.edu.my/id/eprint/38417/1/38417.pdf; http://psasir.upm.edu.my/id/eprint/38417/; https://www.mdpi.com/2073-8994/11/3/381

In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson’s rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods.