Numerical Solutions of Fuzzy Differential Equations by Taylor Method

Abbasbandy, Saeid; Allahviranloo, Tofigh

doi:10.2478/cmam-2002-0006

Cited by 147 publications

(68 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the Theorem 5.4 that was mentioned in [2] convergence of fourth order Runge-Kutta methods followed by Theorem 4.3 in [1] for the convergence of p order Taylor's method, we can define the following theorem related to the convergence of RKM56 in Section 3.…”

Section: Stability Convergence and Error Analysismentioning

confidence: 99%

Numerical solution of nth order fuzzy initial value problems by six stages

Jameel¹,

Anakira²,

Alomari³

et al. 2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

The purpose of this paper is to present a numerical approach to solve fuzzy initial value problems (FIVPs) involving n-th order ordinary differential equations. The idea is based on the formulation of the six stages Runge-Kutta method of order five (RKM56) from crisp environment to fuzzy environment followed by the stability definitions and the convergence proof. It is shown that the n-th order FIVP can be solved by RKM56 by transforming the original problem into a system of first-order FIVPs. The results indicate that the method is very effective and simple to apply. An efficient procedure is proposed of RKM56 on the basis of the principles and definitions of fuzzy sets theory and the capability of the method is illustrated by solving second-order linear FIVP involving a circuit model problem.

show abstract

Section: Stability Convergence and Error Analysismentioning

confidence: 99%

Numerical solution of nth order fuzzy initial value problems by six stages

Jameel¹,

Anakira²,

Alomari³

et al. 2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…The fuzzy differential equation and fuzzy initial value problems are studied by Kaleva [28,29] and Seikkala [36]. Various numerical methods for solving fuzzy differential equations are introduced in [1,2,6,31,32,37]. Very recently Tapaswini and Chakraverty [37] have proposed a new method to solve fuzzy initial value problem.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of n-th Order Fuzzy Linear Differential Equations by Homotopy Perturbation Method

Tapaswini¹,

Chakraverty²

2013

IJCA

View full text Add to dashboard Cite

show abstract

“…Euler numerical technique is used in [23] to solve FDE. Some other numerical techniques, such as Nystrom approach [24], Taylor method [25] and Runge-Kutta approach [26] can also be applied to solve FDEs. However the approximation accuracy of these numerical calculations are normally less.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

Jafari¹,

Yu²,

Li³

et al. 2017

IJCIS

View full text Add to dashboard Cite

The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs) by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs.In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs) with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z-number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.

show abstract

Numerical Solutions of Fuzzy Differential Equations by Taylor Method

Cited by 147 publications

References 8 publications

Numerical solution of nth order fuzzy initial value problems by six stages

Numerical solution of nth order fuzzy initial value problems by six stages

Numerical Solution of n-th Order Fuzzy Linear Differential Equations by Homotopy Perturbation Method

Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

Contact Info

Product

Resources

About