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...

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.

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...

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet...

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...

Problems such as conduction of nerve impulses, behavior of the immune system or of effects of medication, and many others, when modelled by differential equations, are amenable to solution by a mathematical procedure called the decomposition method. This method is efficient and accurate; it makes...