TY - JOUR
T1 - Fuzzy volterra integro-differential equations using general linear method
AU - Majid, Zanariah Abdul
AU - Rabiei, Faranak
AU - Hamid, Fatin Abd
AU - Ismail, Fudziah
N1 - Funding Information:
Acknowledgments: This work was part of FRGS research grant project (Ref: FRGS/2/2013/SG04/UPM/02/1) and the authors wish to thank on Ministry of Higher Education Malaysia for supporting this research.
Funding Information:
Funding: This research was funded by Research University Grant from Research Management Centre of Universiti Putra Malaysia.
Publisher Copyright:
© 2019 by the authors.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - 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 themethod, the numerical results are compared with some existing numerical methods.
AB - 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 themethod, the numerical results are compared with some existing numerical methods.
KW - Fuzzy differential equations
KW - Fuzzy general linear method
KW - Fuzzy volterra integro-differential equations
KW - Generalized Hukuhara differentiability
UR - http://www.scopus.com/inward/record.url?scp=85067296518&partnerID=8YFLogxK
U2 - 10.3390/sym11030381
DO - 10.3390/sym11030381
M3 - Article
AN - SCOPUS:85067296518
SN - 2073-8994
VL - 11
JO - Symmetry
JF - Symmetry
IS - 3
M1 - 381
ER -