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For theguardian.com we had considered and rejected implementing such an explicit scheme for three primary reasons.
A numerical solution, founded on an explicit scheme, is validated.
For the transport step driven by the slow material waves, an explicit scheme is used.
The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost).
Our extensive numerical experiments show that our semi-implicit scheme has much better stability property than an explicit scheme.
Thus the computational cost of our semi-implicit schemes is comparable to that of an explicit scheme.
Similar(16)
The first order differential equations obtained for each control volume are solved by use of a fully explicit scheme using a fourth order Runge Kutta algorithm.
Yet, such heterogeneity index is not able to quantify the surface patterns of a landscape with a fully explicit scheme at each place and scale of the landscape.
The model equations are solved by means of an ADER Discontinuous Galerkin explicit scheme which can, in principle, reach any order of space time accuracy.
As is well known, when (theta=0), (3) is a classical explicit scheme, which has a natural parallelism, but its stability condition is more demanding.
For relatively fine 3-D grids the approach is approximately six times faster than a standard explicit scheme and nearly three times faster than an implicit method employing conjugate gradient iteration at each time step.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com