We consider the problem of computing regular formal solutions of systems of linear differential equations with analytic coefficients. The classical approach consists in reducing the system to an equivalent scalar linear differential equation and to apply the well-known Frobenius method. This transformation to a scalar equation is not necessarily relevant so we propose a generalization of the Fr...

The difficulties with the simple shooting method for the solution of ordinary differential boundary value problems are well known, and there have been many suggested modifications to overcome them. Notable among them are the discrete orthonormalization process of Godunov and Conte (1966), the multiple shooting method (Keller(1968) and Osborne(1969)) and the Riccati transformation method (Scott(...

substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

Microstructure and properties of the Al-6Si-0.3Mg alloys containing scandium (0.2 to 0.6wt %) were investigated. The microstructure was observed by optical microscopy, the hardness was determined by Vickers tester and phase transformation was investigated by differential scanning calorimetry (DSC) technique. The results showed that scandium can refine dendrites, enhance hardness in the aged all...

The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand...

Phase transformation temperature is one of the most important parameters for the shape memory alloys (SMAs). The most popular method to determine these phase transformation temperatures is the Differential Scanning Calorimeter (DSC), but due to the limitation of the DSC testing itself, it made it difficult for the finished product which is not in the powder form. A novel method which uses the U...

In the applications of parallel manipulators, kinematic calibration is required to eliminate the errors resulting from the manufacturing and assembly of both base and tools. In this paper, a calibration method of base and tool transformation is developed by virtue of optical position sensors. An error model for calibration is constructed using differential geometry method. The pose error is obt...

The transformation method has been proposed as a practical tool for the simulation and the analysis of systems with uncertain parameters using fuzzy arithmetic. A major advantage of this method, among others, is the fact that in the analysis part of the method, the degree of influence for each uncertain parameter can be computed with a rather simple formula. However, a thorough examination of h...

Dynamic optimization problems can be numerically solved by direct, indirect and HamiltonJacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant diff...