Laplace transform integration and the slow equations
Seminar Room 1, Newton Institute
We consider the Laplace transform (LT) filtering integration scheme applied to the shallow water equations, and demonstrate how it can be formulated as a finite difference scheme in the time domain by analytical inversion of the transform.
Both Eulerian and semi-Lagrangian versions of the scheme are analyzed. We show the relationship between the LT scheme and the slow equations. We demonstrate the advantages of the LT scheme by means of numerical integrations.