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

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:

Improved Runge-Kutta method , Fuzzy differential equations , Fuzzy volterra integro-differential equations , Generalized Hukuhara differentiability