The algebraic eigenvalue problem
The algebraic eigenvalue problem
Operator splitting and commutativity analysis in the Danish Eulerian model
Mathematics and Computers in Simulation
Wave analysis of different splitting methods in the linearised shallow water equations
International Journal of Computational Science and Engineering
Weighted sequential splittings and their analysis
Computers & Mathematics with Applications
Splitting methods and their application to the abstract cauchy problems
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Additive and iterative operator splitting methods and their numerical investigation
Computers & Mathematics with Applications
Wave analysis of different splitting methods in the linearised shallow water equations
International Journal of Computational Science and Engineering
Application of dynamic diffusion theory in foreign direct investment of Taiwan IC industry in China
International Journal of Computational Science and Engineering
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The shallow water equations describe motions in a shallow, incompressible and nonviscous fluid layer on the rotating Earth. Due to their relative simplicity, they are widely used for testing and analysing new numerical methods developed for weather prediction models. In this paper, we apply different operator splittings, based on directional decomposition, to the linearised form of the shallow water equations obtained by the method of small perturbations. This system has three types of harmonic wave solutions with known dispersion relations and phase velocities. We investigate how the application of operator splitting modifies these important characteristics, and compare the performance of different splitting methods from this point of view.