Search results for "System of differential equations"
showing 8 items of 8 documents
A best proximity point approach to existence of solutions for a system of ordinary differential equations
2019
We establish the existence of a solution for the following system of differential equations (y x ′′((t t ) ) = = g f ((t t ,y x ((t t )) )) ,y x ((t t 0 0) ) = = x x *** in the space of all bounded and continuous real functions on [0, +∞[. We use best proximity point methods and measure of noncompactness theory under suitable assumptions on f and g. Some new best proximity point theorems play a key role in the above result.
Simple differential equations for Feynman integrals associated to elliptic curves
2019
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is therefore of current interest, if these methods extend beyond the case of multiple polylogarithms. In this talk I discuss Feynman integrals, which are associated to elliptic curves and their differential equations. I show for non-trivial examples how the system of differential equations can be brought into an $\varepsilon$-form. Single-scale and multi-scale cases are discussed.
Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with unc…
2013
Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students academic performance in the German region of North Rhine-Westphalia. This approach is supported by the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.
The $\varepsilon$-form of the differential equations for Feynman integrals in the elliptic case
2018
Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The $\varepsilon$-form is obtained by a (non-algebraic) change of basis for the master integrals.
Co-jumps and Markov Counting Systems in Random Environments
2020
Motivated by the analysis of multi-strain infectious disease data, we provide closed-form transition rates for continuous-time Markov chains that arise from subjecting Markov counting systems to correlated environmental noises. Noise correlation induces co-jumps or counts that occur simultaneously in several counting processes. Such co-jumps are necessary and sufficient for infinitesimal correlation between counting processes of the system. We analyzed such infinitesimal correlation for a specific infectious disease model by randomizing time of Kolmogorov’s Backward system of differential equations based on appropriate stochastic integrals.
OPKINE, a multipurpose program for kinetics
1991
The program OPKINE is presented for the study of reaction mechanisms and multicomponent analysis in dynamic conditions. This program is written in FORTRAN-77 for IBM 30/90 and VAX 8300 computers, and permits the simultaneous evaluation of both rate constants and initial reagent concentrations or, alternatively, rate constants and sensitivities. Up to 20 kinetic curves, with up to 400 points each, can be treated to evaluate up to 40 parameters. Integration of the system of differential equations is performed by means of the Runge–Kutta–Fehlberg method. OPKINE is provided with the Simplex, and modified versions of the Davidon–Fletcher–Powell and Gauss–Newton–Marquardt optimization methods. A …
Eine Bemerkung zur Frage der Verwendung Lagrangescher Koordinaten in der Physik nichtlinearer Schwingungen
1958
For the Cartesian coordinates of the elements of a vibrating string, which are introduced as functions of time and a parameter (similar to the Lagrangean method in hydrodynamics), a general, non-linear system of differential equations is offered. The behaviour of the freely vibrating string corresponding to this system agrees, approximately, with the behaviour of a string put in motion in a certain way, which string, if moving freely, would act according to the linear differential equation of the elementary theory.
A deterministic model for highly contagious diseases: The case of varicella
2016
[EN] The classic nonlinear Kermack-McKendrick model based upon a system of differential equations has been widely applied to model the rise and fall of global pandemic and also seasonal epidemic by introducing a forced harmonic infectivity which would change throughout the year. These methods work well in their respective domains of applicability, and for certain diseases, but they fail when both seasonality and high infectivity are combined. In this paper we consider a Susceptible-Infected-Recovered, or SIR, model with two latent states to model the propagation and evolutionary history of varicella in humans. We show that infectivity can be calculated from real data and we find a nonstanda…