We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

In the present paper, hybrid differential transform and finite difference method (HDTFD) is applied to solve 2D transient nonlinear straight annular fin equation. For the case of linear heat transfer the results are verified with analytical solution. The effect of different parameters on fin temperature distribution is investigated. Effect of time interval of differential transform on the stabi...

in this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. in proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. in comparison with existing similar neural networks proposed model provides solutions with high accuracy. numerica...

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

In this paper we study numerical methods for hybrid fuzzy fractional differential equation, Degree of Sub element hood and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition.

In this paper we study numerical methods for hybrid fuzzy fractional differential equations and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition. We consider a differential equation of fractional order and we compared the results with their exact solutions in order to demonstrate the validity and applicability of the method....

We investigate the invariance properties of a class of switched systems where the value of a switching signal determines the current mode of operation (among a finite number of them) and, for each fixed mode, its dynamics are described by a Differential Algebraic Equation (DAE). Motivated by the lack of invariance principles of switched DAE systems, we develop such principles for switched DAE s...

In previous work we demonstrated that reachability algorithms using level set methods and based on the Hamilton-Jacobi PDE can be adapted to systems whose dynamics are described by differential algebraic equations. Here we extend those results to hybrid systems. The only significant addition required is a mechanism for handling the state reset that occurs during discrete jumps between modes. We...

A compositional interchange format for hybrid systems is defined in terms of an interchange automaton, allowing arbitrary differential algebraic equations, including fully implicit or switched DAEs, discrete, continuous and algebraic variables, that can be internal or external, urgency conditions, and operators for parallel composition, action hiding, variable hiding and urgent actions. Its com...