Journal of Applied and Computational Mechanics

Numerical Simulation of Fuzzy Volterra Integro-differential ‎Equation using Improved Runge-Kutta Method

Document Type : Research Paper

Authors

1 School of Engineering, Monash University Malaysia, 47500, Selangor, Malaysia

2 Institute of Mathematical Research, Universiti Putra Malaysia, 43400, Selangor, Malaysia‎

3 Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China,‎ Chengdu, 610054, Sichuan, PR China‎

4 Faculty of Mechanical and Industrial Engineering, Quchan University of Technology, Quchan, Iran

5 Department of Mathematics, University of Malakand, Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan

6 Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran‎

7 Department of Information Technology, Malaysia University of Science and Technology, 47810, Selangor, Malaysia‎

Abstract

In this research, fourth-order Improved Runge-Kutta method with three stages for solving fuzzy Volterra integro-differential (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. Based on the obtained results, it is clear that the fourth-order Improved Runge-Kutta method with higher accuracy and less number of stages which leads the less computational cost is more efficient than other existing methods for solving FVID equations.

Keywords

Main Subjects

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Journal of Applied and Computational Mechanics
Volume 9, Issue 1
January 2023
Pages 72-82