In this paper, a novel, simple yet efficient method is proposed to approximately solve linear ordinary differential equations (ODEs). Emphasis is put on second-order linear ODEs with variable coefficients. First, the ODE to be solved is transformed to either a Volterra integral equation or a...

The paper presents significant aspects of analytical and numerical simulation of a high-frequency converter with voltage-fed inverter, framing in over 10 years preoccupations of the Electric Powers Laboratory from our Technical University. Here some constructive-functional aspects are...

This report presents a method of constructing approximate symmetries and invariants in dynamical systems. At first, a similar approach was developed for linear systems (for example, the time-dependent invariants by Leach and Lewis). Beam line systems are considered as an example of such...

Large-scale air pollution models can successfully be used in different environmental studies. These models are described mathematically by systems of partial differential equations. Splitting procedures followed by discretization of the spatial derivatives lead to several large systems of...

We consider an autonomous system of ordinary differential equations near its stationary point. By means of the formal change of coordinates, we can transform the system into its normal form. By means of the power transformation of coordinates, the normal form is reducd to a problem of less...

In this paper, we present an algorithm to simplify a first-order system of two ordinary differential equations in the neighborhood of singular points with evidence, we prove a theorem dealing with its convergence and compare it with already known methods and apply it to some particular systems.

Excessive temperatures in cable bundles integrated in cars can cause harms to connecting structures and essential components. To avoid hotspot generation already at the production of cable harnesses, reliable predictions of temperatures in cables under load are necessary. Two approaches for...

An analytical solution of the partial differential equation describing the enthalpy balance of the cooling fluid in a batch exothermic reactor has been developed for a constant flow. Thanks to an analytical integration on position, the simulation of the process can be performed with one...

Global sensitivity indices for rather complex mathematical models can be efficiently computed by Monte Carlo (or quasi-Monte Carlo) methods. These indices are used for estimating the influence of individual variables or groups of variables on the model output.

Detailed knowledge about the function and morphology of temporomandibular joint are necessary for clinical applications and for analyses of the function of temporomandibular joint prosthesis. Movements of temporomandibular joint are biomechanically sophisticated and are up-to-date not clear....