In this paper, we for the first time propose a dynamical system (DS) approach to describe the time variation of the coach travel. This dynamical study for the analysis and modeling is of several advantages. First, it can be used for dynamical analysis, such as quantitative, stability, and equilibrium analysis. Second, it can be further applied to analyze the competition behaviors among various ...

Differential equations arise in mathematics, physics, medicine, pharmacology, communications, image processing and animation, etc. An Ordinary Differential Equation (ODE) is a differential equation if it involves derivatives with respect to only one independent variable which can be studied from different perspectives; such as: analytical methods, graphical methods and numerical methods. This r...

The stationary flow of a jet of a Newtonian fluid that is drawn by gravity onto a moving surface is analyzed. It is assumed that the jet has a convex shape and hits the moving surface tangentially. The flow is modelled by a third-order ODE on a domain of unknown length and with an additional integral condition. By solving part of the equation explicitly, the problem is reformulated as a first-o...

Abstract. The first order nonlinear ODE φ̇(t) + sinφ(t) = q(t), q(t) = B +A cosωt, where A, B, ω are real constants, is considered, the transformation converting it to a second order linear homogeneous ODE with polynoimial coefficients is found. The latter is identified as a particular case of the double confluent Heun equation. The series of algebraic constraints on the constant parameters is f...

The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman’s original development. In the time-slicing approximation the quantum mechanical evolution will generally not have any stationary states. We look for conditions on the potential energy term such that the quantum mechanical evolution m...

We propose a model order reduction (MOR) approach for networks containing simple and complex components modeled by linear ODE and nonlinear PDE systems respectively. These systems are coupled through the network topology using the Kirchhoff laws. We consider as application MOR for electrical networks, where semiconductors form the complex components. POD combined with discrete empirical interpo...