Notes on the Solutions of PDE Systems—Duality Between Two Worlds

  • Viktor JózsaEmail author
  • Róbert Kovács
Part of the Power Systems book series (POWSYS)


In the engineering practice, most of the problems are solved using a commercial software such as finite element codes. In parallel, these software behave like a ‘black box’, offering only minimal insight into what equations are solved at the background. This is crucial in some problems, mainly when a non-classical (extended) material model must be applied. Using commercial software makes the treatment more rigid and limited, which is sometimes not the most efficient tool. Thus it could be necessary to write your code to obtain the solution. This chapter introduces the reader into the fundamental aspects of numerical (and analytical) methods and presents the properties of some particular numerical schemes, for instance, stability, dissipation, and dispersion.


Finite differences Finite elements Boundary conditions Stability Diffusion Dispersion 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Energy Engineering, Faculty of Mechanical EngineeringBudapest University of Technology and EconomicsBudapestHungary

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