Application of Adomian decomposition method to solve hybrid fuzzy differential equations

AbstractIn this paper, we study the numerical solution of hybrid fuzzy differential equations by using Adomian decomposition method (ADM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from ADM and predictor corrector method (PCM), we have studied their accuracy

Multistep block method for solving Volterra integro-differential equations

In this paper, we use multistep block method for solving linear and non-linear Volterra integro-differential equations (VIDEs) of the second kind. The VIDEs will be solved by using the combination of multistep block method of order three and Newton-Cotes quadrature rule of suitable order. The proposed method will solve VIDEs for K (x, s) = 1 and K (x, s) ≠ 1. The stability region of the method will be given. Numerical problems are included to represent the performance of the proposed method

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515

Non-constructive interval simulation of dynamic systems

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Numerical solution of fuzzy delay differential equations under generalized differentiability by Euler's method

In this paper, we interpret a fuzzy delay differential equations using the concept of generalized differentiability. Using the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. The Euler approximation method is implemented and its error analysis is discussed. The applicability of the theoretical results is illustrated with some examples

Numerical Solution of Fuzzy Differential Equations Based on Taylor Series by Using Fuzzy Neural Networks

In this paper a new method based on learning algorithm of Fuzzy neural network and Taylor series has been developed for obtaining numerical solution of fuzzy differential equations.A fuzzy trial solution of the fuzzy initial value problem is written as a sum of two parts.The first part satisfies the fuzzy initial condition,it contains Taylor series and involves no fuzzy adjustable parameters.The second part involves a feed-forward fuzzy neural network containing fuzzy adjustable parameters (the fuzzy weights).Hence by construction,the fuzzy initial condition is satisfied and the fuzzy network is trained to satisfy the fuzzy differential equation . In comparison with existing similar neural networks,the proposed method provides solutions with high accuracy.Finally , we illustrate our approach by two numerical examples

Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays

In this research, a new method to solve the Fuzzy Delay Differential Equations (FDDEs) with unknown state-delays constrained optimization problem is introduced. This method is based on the coupling of second and third orders Runge- Kutta (RK) method called hybrid RK method. The main goal of this thesis is to identify the unknown state-delays using experimental data. RK methods are chosen because they are well-established and can be easily modified to overcome the discontinuities which occur in Delay Differential Equations (DDEs) especially outside uniform nodes with delay step-size. Numerical results of FDDEs from the hybrid RK methods are compared with exact solutions derived from stepwise approach using Maple software. The relative errors are calculated for the purpose of accuracy checking on these numerical schemes. In this study, a dynamic optimization problem in which the state-delays are decision variables is also imposed; with its formulated cost function. The gradient of the cost function is computed by solving auxiliary FDDEs. By exploiting the results, the state-delay identification problem can be solved efficiently and accurately using a gradient-based optimization method. In addition, a C program has been developed based on hybrid RK methods for solving these problems. Consequently, the results show that the new hybrid scheme is an efficient numerical technique in solving all the problems above with acceptable errors