Operator splitting and commutativity analysis in the Danish Eulerian Model Original Research Article

In this paper the splitting error arising in the Danish Eulerian Model is investigated. Sufficient conditions under which the local splitting error vanishes are formulated for the continuous case. The numerical solution of the model problem introduces several other error sources, which makes the task of determining the effect of the splitting error more complicated. Therefore, we need numerical examples which will allow us to separate the splitting errors from the other errors in order to evaluate both the magnitude of these errors and the relationships between splitting errors and other errors for different values of the discretization parameters. Several such examples have been constructed and analysed. The appropriate conclusions were drawned. The experiences obtained from these experiments can be a starting step towards a total error analysis of the numerical solution of split systems of partial differential equations.