Abstract
This study presents solution for the first order hybrid fuzzy differential equation by Runge-Kutta method of order two with new parameters and Harmonic mean of kis which are used in the main formula in order to increase the order of accuracy of the solution. This method is discussed in detail followed by a complete error analysis. The accuracy and efficiency of the proposed method is illustrated by solving a fuzzy initial value problem.
Highlights
This study presents solution for the first order hybrid fuzzy differential equation by Runge-Kutta method of order two with new parameters and Harmonic mean of ki’s which are used in the main formula in order to increase the order of accuracy of the solution
The use of Hybrid Fuzzy Differential equations is a natural way to model control systems with embedded uncertainty that are capable of controlling complex systems which have discrete event dynamics as well as continuous time dynamics
We develop numerical method for hybrid fuzzy differential equations by an application of the Runge-Kutta method of order two with new
Summary
In recent years many works have been performed by several authors in numerical solutions of fuzzy differential equations. An arbitrary fuzzy number is represented by an ordered pair of functions (u (r),u (r)) , 0 ≤ r ≤ 1 that satisfies the following requirements: parameters and Harmonic mean of ki’s which are used in the main formula in order to increase the order of accuracy of the solution. Using a representation of fuzzy numbers we may represent x∈E by a pair of functions (x (r),x (r)),0 ≤ r ≤ 1, such that: the r-level set is [u]r = {x\u(x) ≥ r}, 0 ≤ r ≤ 1 is a closed and bounded interval denoted by [u]r u (r), u (r) and clearly, [u]0 = {x|u(x) > 0} is compact
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