The objective of the article is the numerical analysis of the absolute controllability of a parabolic system with delayed controls and non zero boundary conditions. Precisely the non zero Dirichlet conditions for the considered PDE are the main novelty of the article. As a result we gave the conditions of the controllability for the parabolic PDE with delayed controls. Key-Words: Controllabilit...

In this work we introduce and perform a study on the multitime multi-objective fractional variational problem of minimizing a vector of quotients of path independent curvilinear integral functionals (MFP ) subject to certain partial differential equations (PDE) and/or partial differential inequations (PDI), using a geometrical language. The paper is organized as follows: §1 formulates a PDI&PDE...

This notation is slightly confusing, since L is not a matrix: we use it to denote this \a ne linear" operation. To solve this system of ODEs, we choose a time step k, de ne time levels tn = nk for n = 0, 1, . . . , and introduce u n ∈ RN−1. The vector un will be determined by a discrete dynamical system and it is our hope that this can be done in such a way that uj ≈ Uj(tn) ≈ u(xj, tn). Recall ...

A thermal–electrochemical model of lithium-ion batteries is presented and a Luenberger observer is derived for State-of-Charge (SoC) estimation by recovering the lithium concentration in the electrodes. This first-principles based model is a coupled system of partial and ordinary differential equations, which is a reduced version of the Doyle–Fuller–Newman model. More precisely, the subsystem o...

Pulse detonation technology can be a revolutionary approach for propulsion system since it offers significant fuel efficiency, higher thrust to weight ratio and low cost. Although the design concept of a pulse detonation engine is comparatively simple, but the development and stabilization of sustainable detonation wave front is difficult. Consequently pulse detonation engine technology is stil...

In the present paper a bicriterial optimal control problem governed by a parabolic partial differential equation (PDE) and bilateral control constraints is considered. For the numerical optimization the reference point method is utilized. The PDE is discretized by a Galerkin approximation utilizing the method of proper orthogonal decomposition (POD). POD is a powerful approach to derive reduced...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...