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[CT016]

Session Date & Time : 1E (Aug.21, 17:40-19:20)
Type : Contributed Talk
Abstract : In this study, we consider a system of second kind linear Fredholm integral equations with Green’s type kernel function. We propose a piecewise polynomial based Galerkin and iterated Galerkin methods to solve the integral model. We carry out the convergence and error analysis for the proposed methods and establish the superconvergence results for iterated Galerkin method. The theoretical results are supported by numerical tests.
Classification : 34A12, 45F15
Author(s) :
- Rakesh Kumar (Indian Institute of Technology, Kanpur (India))
- Kapil Kant (Indian Institute of Technology, Kanpur (India))
- B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))

Session Date & Time : 1E (Aug.21, 17:40-19:20)
Type : Contributed Talk
Abstract : We consider an impulsive-differential-equation system, based on SIS model, to describe the spread of pathogens in healthcare systems accounting for patient mobility. We propose sufficient conditions guaranteeing network suppression of infection and an algorithm to indicate hospitals prone to high bacteria prevalence and ultimately to ensure the stability of a disease-free state. As an illustration, we present a model of hospital-acquired multidrug-resistant bacteria transmission based on hospital admission records provided by a German insurance company.
Classification : 34A37, 65P40, 92D30
Author(s) :
- Monika Joanna Piotrowska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
- Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
- Konrad Sakowski (Institute of Applied Mathematics and Mechanics, University of Warsaw and Institute of High Pressure Physics, Polish Academy of Sciences)

Session Date & Time : 1E (Aug.21, 17:40-19:20)
Type : Contributed Talk
Abstract : Understanding the dynamics of plasma is crucial in many concurrent applications. Those include astrophysics, space discovery, and designing fusion reactors. Numerical methods are a great tool for this purpose. In this talk, an efficient numerical method based on Galerkin approximations is presented. The method has high accuracy, capability of capturing shocks and turbulence, and consistency with thermodynamics. We show several interesting numerical simulations to demonstrate those properties.
Classification : 34A45
Author(s) :
- Tuan Anh Dao (Uppsala University)

Session Date & Time : 1E (Aug.21, 17:40-19:20)
Type : Contributed Talk
Abstract : I will introduce an ODE model describing the spread of multidrug-resistant bacteria in a hospital network. I will present the mathematical properties of the model solutions, including the global stability of steady states. Based on simulations for real-life data, I will describe how the parameters affect the process dynamics at both network and hospital levels. Finally, the relations to other types of models describing similar processes will be discussed.
Classification : 34Axx, 34Cxx, 34D23, 92D30
Author(s) :
- Agata Lonc (University of Warsaw)
- Monika Joanna Piotrowska (Institute of Applied Mrsaathematics and Mechanics, University of Waw)
- Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)

Session Date & Time : 1E (Aug.21, 17:40-19:20)
Type : Contributed Talk
Abstract : This presentation explains the fundamentals of Artificial Neural Networks using fractional differential equations (FDEs). The role of FDEs in machine learning algorithms to build intelligent machines to imitate complex human tasks like vision, motor control, or language understanding is demonstrated. Applications in image processing are given by developing the fractional-order derivative masks to enhance the features of the crop leaf disease prediction models. Also, numerical simulations are presented to validate the theoretical results.
Classification : 34Axx, 68Txx, 92-XX
Author(s) :
- Balasubramaniam Pagavathi gounder (The Gandhigram Rural Institute (Deemed to be University))