Abstract In this paper, we propose an efficient approach to solve the fifthorder KdV equations. By using the variational iteration method, the exact solutions of the fifth-order KdV equations are given without the calculation of the complicated Adomian’s polynomials, linearization, discretization, weak nonlinearity assumptions or perturbation theory. Numerical examples are presented that show t...

!Istituto Chimica Tecnologia Prodotti Naturali, C.N.R. (associated with Istituto Nazionale Chimica Sistemi Biologici, C.N.R.), 153 La Malfa, 90146 Palermo, Italy "Science Exact Institute, Chemistry Department, Oum El Bouaghi University, Oum El Bouaghi 04000, Algeria #Dipartimento Chimica Organica, Universita% Palermo, Viale d.Scienze, 90128 Palermo, Italy $Jodrell Laboratory, Royal Botanic Gard...

The increasing share of volatile renewable electricity production motivates demand response. Substantial potential for response is offered by flexible processes and their local multi-energy supply systems. Simultaneous optimization schedules can exploit the potential, but leads to numerically challenging problems nonlinear dynamic processes. In this paper, we propose capture process dynamics us...

In this paper we discuss di erent control design methods for nonlinear control systems. We focus our attention on passivity-based control and the feedback linearization approach for solving set-point and tracking control problems. We also consider the case of model and parameter uncertainties. We concentrate on Euler-Lagrange systems which is a fairly wide and illustrative class of nonlinear sy...

The exact solution of the reliability of structures under stochastic loading is generally difficult, and various approximate methods have been developed. The most popular are the linearization method, the Monte-Carlo method and its numerous variants. In this paper new modification of the Monte-Carlo method based on asymptotical expansion is examined. Results of mathematical simulation are given.

We present a new class of exponential integrators for ordinary differential equations: locally exact modifications of known numerical schemes. Local exactness means that they preserve the linearization of the original system at every point. In particular, locally exact integrators preserve all fixed points and are A-stable. We apply this approach to popular schemes including Euler schemes, impl...

In recent years, it has been found that derivatives of non-integer order are very effective for the description of many physical phenomena such as rheology, damping laws, and diffusion processes. These findings invoked the growing interest on studies of the fractal calculus in various fields such as physics, chemistry, and engineering [1 – 4]. In general, there exists no method that yields an e...

In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent s...