Abstract
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.
Highlights
Fuzzy differential equations (FDEs) and fuzzy integral equations (FIEs) have been extensively studied in the past few years
We propose the numerical solutions of fuzzy Volterra integro-differential equations (FVIDEs) using the general linear method (GLM) introduced by Butcher in [17]
Symmetry 2019, 11, 381 the GLM was studied for finding the numerical solutions of FDEs by Rabiei et al in [18] and based on that, in this paper we develop the fuzzy third-order GLM together with suitable integration method to solve FVIDEs
Summary
Fuzzy differential equations (FDEs) and fuzzy integral equations (FIEs) have been extensively studied in the past few years. FIDEs take the form of both FDEs and FIEs. A particular class of FIDEs is known as fuzzy Volterra integro-differential equations (FVIDEs). In [13], Allahviranloo et al proposed a new technique to solve the FVIDEs using definition of generalized differentiability. We propose the numerical solutions of FVIDEs using the general linear method (GLM) introduced by Butcher in [17]. Symmetry 2019, 11, 381 the GLM was studied for finding the numerical solutions of FDEs by Rabiei et al in [18] and based on that, in this paper we develop the fuzzy third-order GLM together with suitable integration method to solve FVIDEs. In Section 2, preliminaries on fuzzy numbers and theories are proposed.
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