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The computational algorithm is based on the leapfrog time stepping scheme with unstaggered temporal grids.
Using leapfrog time integration, we obtain a mixed E−B finite-element time-domain scheme for the full-discrete Maxwell's equations.
Invoking appropriate mass-lumping concepts then leads to an explicit leapfrog time stepping algorithm for the amplitudes of the basis functions.
The instability of Fornberg's pattern for leapfrog time integration of the nonlinear convective equation ∂u/∂t + u∂u/∂x = 0 is found to occur as a closed three-mode process and to include the sideband instability.
In the first part of this paper, we compare the stability and accuracy of second- and fourth-order-accurate spatial central discretizations on staggered grids with a third-order-accurate spatial discretization on an unstaggered grid, combined with a second-order leapfrog time integration scheme for modeling linear dispersive phenomena in a one-dimensional single-resonance Lorentz medium.
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An Arakawa B-grid is used in the horizontal directions and leapfrog time-stepping.
Nevertheless, Kent's 10 bonus points were enough to leapfrog long-time Division Two leaders, Essex, into the promotion slot, albeit having played a game more.
The story leapfrogs through time taking surprising turns, contrasting – with the lightest of touches – the different, and evolving, life chances of the haves and the have-nots, of boys and girls.
The leapfrogging through time in "The Audience" — especially as embodied by its leading lady – is a virtuoso version of what happens every time a performer convinces us that she's someone else, existing in a breathing moment that only those of us who are gathered in this place at this time have access to.
The story of Mae leapfrogs in time, showing her at one instant as a pushy young hopeful in vaudeville and the next as the stylized gargoyle of her old age, with Mr. Chamberlin and the invaluable Bob Stillman (also the show's musical director) portraying human stepping stones and resting places along Mae's path to legendhood.
This spatial approximation, combined with a leapfrog scheme in time, leads also to a fast explicit and accurate method.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com