Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method

Abstract

In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

“…In this section, we formulate the trial and error function of ChNN method to approximate nonlinear nth order FDEs. Analytical and numerical investigations of nth order FDEs are accomplished by various authors, for instance, Jayakumar et al [10] used Runge-Kutta method of order five to numerically solve nth order FDEs, Salahshour [25] proposed an integral form to examine analytical solutions of these equations, Ahmady [26] proposed piecewise approximation method to discuss the solutions of nth order FDEs etc. Comparatively, ChNN for its less computational complexity, executes the appropriate analytical approximations more rapidly.…”

“…In recent times, many ways and means are being established to analyze and simulate fuzzy differential equations. For instance, Euler type methods [4], shooting method [5], fuzzy Picard method [6], fuzzy Laplace transform [7], fuzzy Sumudu transform [8], Runge-Kutta method [9]- [10], fuzzy variational iteration method [11], Adams predictor corrector [12], Taylor method [13], modified Homotopy perturbation method [14], to name a few. Along with these techniques, various papers are found where the latest methods, like different artificial neural networks [15]- [16], are also carried out for the evaluation of FDEs.…”

Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

“…Runge-Kutta-Fehlberg method for hybrid fuzzy differential equation is solved by Jayakumar and Kanagarajan [41]. A different approach followed by Runge-Kutta method is applied by Akbarzadeh Ghanaie and Mohseni Moghadam [42].…”

Solving hybrid fuzzy differential equations by Chebyshev wavelet

“…Therefore, they have a wide range of applications in science and engineering. So far, many numerical methods have been applied by several researchers to solve these equations such as, Euler method presented in [2,18], Nyström method presented in [23], Runge-Kutta method presented in [1,19], Runge-Kutta Fehlberg presented in [12], the improved predictor-corrector presented in [14], Haar wavelet presented in [17].…”