Hybrid Fuzzy Differential Equations Research Articles

Numerical solution of hybrid fuzzy differential equations using improved predictor–corrector method

The hybrid fuzzy differential equations have a wide range of applications in science and engineering. This paper considers numerical solution for hybrid fuzzy differential equations. The improved predictor–corrector method is adapted and modified for solving the hybrid fuzzy differential equations. The proposed algorithm is illustrated by numerical examples and the results obtained using the scheme presented here agree well with the analytical solutions. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated calculations of algorithm.

Euler method for solving hybrid fuzzy differential equation

In this paper, we study the numerical method for solving hybrid fuzzy differential using Euler method under generalized Hukuhara differentiability. To this end, we determine the Euler method for both cases of H-differentiability. Also, the convergence of the proposed method is studied and the characteristic theorem is given for both cases. Finally, some numerical examples are given to illustrate the efficiency of the proposed method under generalized Hukuhara differentiability instead of suing Hukuhara differentiability.

The Nyström method for hybrid fuzzy differential equation IVPs

In this paper, the Nyström method is developed to approximate the solutions for hybrid fuzzy differential equation initial value problems (IVPs) using the Seikkala derivative. A proof of convergence of this method is also discussed in detail. The accuracy and efficiency of the proposed method are demonstrated by applying it to two different numerical experiments.

Numerical solution of hybrid fuzzy differential equations by predictor-corrector method

In this paper, we study the numerical solution of hybrid fuzzy differential equations by using Adams–Bashforth, Adams–Moulton and predictor-corrector methods. Predictor-corrector is obtained by combining Adams–Bashforth and Adams–Moulton methods. In addition, we state the convergence and stability of the proposed methods. Examples are presented to illustrate the computational aspects of these methods.

Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem

In this paper, we study hybrid fuzzy differential equation initial value problems (IVPs). We consider the problem of finding their numerical solutions by using a recent characterization theorem of Bede for fuzzy differential equations. We prove a corollary to Bede’s characterization theorem and give a characterization theorem for hybrid fuzzy differential equation IVPs. Then we prove that any suitable numerical method for ODEs can be applied piecewise to numerically solve hybrid fuzzy differential equation IVPs. Numerical examples are provided which connect the new results with previous findings.

The Runge–Kutta method for hybrid fuzzy differential equations

In this paper we study numerical methods for addressing hybrid fuzzy differential equations by an application of the Runge–Kutta method for fuzzy differential equations using the Seikkala derivative. We state a convergence result and give a numerical example to illustrate the theory.

Numerical solution to hybrid fuzzy systems

In this paper we study numerical methods for hybrid fuzzy differential equations by an application of the Euler method for fuzzy differential equations. We prove a convergence result and give several numerical examples to illustrate the theory.