Methods for solving mathematical physics problems

The book examines the classic and generally accepted methods for solving mathematical physics problems (method of the potential theory, the eigenfunction method, integral transformation methods, discretisation characterisation methods, splitting methods). A separate chapter is devoted to methods for solving nonlinear equations. The book offers a large number of examples of how these methods are applied to the solution of specific mathematical physics problems, applied in the areas of science and social activities, such as energy, environmental protection, hydrodynamics, theory of elasticity, etc

Quality criteria for mathematical models in relation to models' purposes:Their usefulness in higher engineering eduaction

A taxonomy of eight quality criteria for mathematical models was developed for the common basic modelling course in the innovated BSc curriculum of the Eindhoven University of Technology. First year engineering students of all disciplines reflected on their modelling group projects, answering the question how their models could be improved, using the criteria. The students were also asked to indicate the purpose(s) of their models from a list of 16 purposes. This study explores the purposes’ and criteria’s usefulness, defined as relevance combined with understandability. The purpose of optimization proved to be most relevant, followed by analysis, prediction (what), and verification.The criteria of specialization, genericity, scalability, distinctiveness, and convincingness proved to be useful, the criteria of audience, impact, and surprise did not

Heterogeneous mathematical models in fluid dynamics and associated solution algorithms

Mathematical models of complex physical problems can be based on heterogeneous differential equations, i.e. on boundary-value problems of different kind in different subregions of the computational domain. In this presentation we will introduce a few representative examples, we will illustrate the way the coupling conditions between the different models can be devised, then we will address several solution algorithms and discuss their properties of convergence as well as their robustness with respect to the variation of the physical parameters that characterize the submodel