Suche
Anzeige der Dokumente 1-2 von 2
Aufsatz
A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics
(2022-01-03)
Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date, emanating from both applied mathematics and mechanics communities. Although considering the same problem, the given complex potentials prove to be different, revealing various inconsistencies in terms of resulting stresses and displacements. Essential information on ...
Aufsatz
A Stability Analysis of Modified Patankar–Runge–Kutta methods for a nonlinear Production–Destruction System
(2023-03-24)
Modified Patankar–Runge–Kutta (MPRK) methods preserve the positivity as well as conservativity of a production–destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do not belong to the class of general linear methods, i. e. the iterates are generated by a nonlinear map g even when the PDS is linear. Moreover, due to the conservativity of the method, the map g possesses non-hyperbolic fixed points.
Recently, a new theorem for the investigation of ...