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

Faranak Rabiei, Fatin Abd Hamid, Mohammad Mehdi Rashidi, Zeeshan Ali, Kamal Shah, Kamyar Hosseini, Touraj Khodadadi

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)72-82
Number of pages11
JournalJournal of Applied and Computational Mechanics
Volume9
Issue number1
DOIs
Publication statusPublished - Jan 2023

Keywords

  • Fuzzy differential equations
  • Fuzzy volterra integro-differential equations
  • Generalized hukuhara differentiability
  • Improved runge-kutta method

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