TY - JOUR
T1 - Numerical Simulation of Fuzzy Volterra Integro-differential Equation using Improved Runge-Kutta Method
AU - Rabiei, Faranak
AU - Hamid, Fatin Abd
AU - Rashidi, Mohammad Mehdi
AU - Ali, Zeeshan
AU - Shah, Kamal
AU - Hosseini, Kamyar
AU - Khodadadi, Touraj
N1 - Publisher Copyright:
© 2021 Shahid Chamran University of Ahvaz, Ahvaz, Iran. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0 license) (http://creativecommons.org/licenses/by-nc/4.0/).
PY - 2023/1
Y1 - 2023/1
N2 - In this research, fourth-order Improved Runge-Kutta method with three stages for solving fuzzy Volterra integrodifferential (FVID) equations of the second kind under the concept of generalized Hukuhara differentiability is proposed. The advantage of the proposed method in this study compared with the same order classic Runge-Kutta method is, Improved Runge- Kutta (IRK) method uses a fewer number of stages in each step which causes less computational cost in total. Here, the integral part is approximated by applying the combination of Lagrange interpolation polynomials and Simpson’s rule. The numerical results are compared with some existing methods such as the fourth-order Runge-Kutta (RK) method, variational iteration method (VIM), and homotopy perturbation method (HPM) to prove the efficiency of IRK method.
AB - In this research, fourth-order Improved Runge-Kutta method with three stages for solving fuzzy Volterra integrodifferential (FVID) equations of the second kind under the concept of generalized Hukuhara differentiability is proposed. The advantage of the proposed method in this study compared with the same order classic Runge-Kutta method is, Improved Runge- Kutta (IRK) method uses a fewer number of stages in each step which causes less computational cost in total. Here, the integral part is approximated by applying the combination of Lagrange interpolation polynomials and Simpson’s rule. The numerical results are compared with some existing methods such as the fourth-order Runge-Kutta (RK) method, variational iteration method (VIM), and homotopy perturbation method (HPM) to prove the efficiency of IRK method.
KW - Fuzzy differential equations
KW - Fuzzy volterra integro-differential equations
KW - Generalized hukuhara differentiability
KW - Improved runge-kutta method
UR - https://www.scopus.com/pages/publications/85140016123
U2 - 10.22055/jacm.2021.38381.3212
DO - 10.22055/jacm.2021.38381.3212
M3 - Article
AN - SCOPUS:85140016123
SN - 2383-4536
VL - 9
SP - 72
EP - 82
JO - Journal of Applied and Computational Mechanics
JF - Journal of Applied and Computational Mechanics
IS - 1
ER -