In this research field we want to apply the mathematical modelling approach to real world practical problems of social sciences, like opinion formation in society, predicting cocaine consumption, modelling the effects of a smoke-free legilation, investigation of dynamics and sociocultural characteristics of infant obesity, etc. The goal here is to develop better models adequate to describe reality and make improved predictions and assessments to show how social problems, stakeholders or political decision makers could benefit from a mathematical modelling approach.
Hereby we pay special attention to environmental and socio-economic models, like operational model for integrated (water/energy/clean air) resources management taking into account the changing climatic and socio-economic conditions in the considered system.
Most of the models are nonlinear systems of ordinary differential equations. We design nonstandard finite difference schemes (NSFD) to solve them adequately, e.g. preserving the positivity of the solution.
People in Group
- Michael Günther
- Matthias Ehrhardt
- Rafael Villanueva, Institute for Multidisciplinary Mathematics Valencia, Spain.
- J.-C. Cortés, M. Ehrhardt, A. Sánchez-Sánchez, F.-J. Santonja and R.-J. Villanueva, Modelling the dynamics of the students academic performance in the German region of North Rhine-Westphalia: an epidemiological approach with uncertainty, accepted: Int. J. Comput. Math. (2013).
- J.-C. Cortés, M. Ehrhardt, A. Sánchez-Sánchez, F.-J. Santonja and R.-J. Villanueva, Modelling the dynamics of the students academic performance in the German region of North Rhine-Westphalia, Proceedings of the CMMSE 2012 - 12th International Conference Computational and Mathematical Methods in Science and Engineering, July 2-5, La Manga - Murcia, Spain, ISBN 978-84-615-5392-1.
- M. Ehrhardt, M. Peco, A.-C. Tarazona, R.-J. Villanueva and J. Villanueva-Oller Short Term Prediction of a Dynamic Radicalization Model applied to the current situation in the Basque Country, Nonstandard Finite Difference Schemes for the Black-Scholes Equation, Chapter in: J.C. Cortés, L. Jodar Sánchez and R.J. Villanueva (eds.), Mathematical Modeling in Engineering & Social Sciences, Nova Science, 2014.
- Tanja Deutsch, Mathematische Modellierung von Radikalisierungsprozessen am Beispiel von rechtsradikalen Gruppierungen in Deutschland Bachelorarbeit Bergische Universität Wuppertal, in Arbeit.