2008-04-17Zeitschriftenartikel DOI: 10.18452/9451
Fourth-Order Splitting Methods for Time-DependantDifferential Equations
Mathematisch-Naturwissenschaftliche Fakultät II
This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes, e.g., wave-propagation or heat-transfer, that are modeled by wave equations or heat equations. Here, we study both parabolic and hyperbolic equations. We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods, which are standard splitting methods of lower order, e.g. second-order. Our aim is to develop higher-order ADI methods, which are performed by Richardson extrapolation, Crank-Nicolson methods and higher-order LOD methods, based on locally higher-order methods. We discuss the new theoretical results of the stability and consistency of the ADI methods. The main idea is to apply a higherorder time discretization and combine it with the ADI methods. We also discuss the discretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives. The higher-order methods are unconditionally stable. Some numerical experiments verify our results.
Dateien zu dieser Publikation
Anzeige der Publikationen mit ähnlichem Titel, Autor, Urheber und Thema.
2011-09-27BuchSplitting Method of Convection-Diffusion Methods with Disentanglement methods Disentanglement MethodsGeiser, Jürgen; Elbiomy, MahmoudIn this paper, we discuss higher-order operator-splitting methods done by disentanglement methods. The idea is based on computing best fitted exponents to an exponential splitting scheme with more than two operators. We ...
1983-01-01ZeitschriftenartikelA New Biometrical Procedure for Testing the Equality of Measurements from Two Different Analytical Methods. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part I Passing, H.; Bablok, W.
1974-01-01ZeitschriftenartikelEine Methode zur direkten Bestimmung des Creatinins in Serum und Harn ohne Enteiweißung nach einer modifizierten Jaffé-Methode Helger, R.; Rindfrey, H.; Hilgenfeldt, J.