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On a finite difference scheme for Burgers’ equation
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A New Finite-Difference Diffusion Scheme
Journal of Computational Physics, 1996The authors purpose a new second-order accurate, explicit finite difference diffusion scheme, that they call ``three-level, locally implicit'' scheme. The scheme is derived as a weighted average of the conventional forward-in-time, explicit diffusion scheme over one grid length and the same scheme over two grid lengths.
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To arrive at finite difference equations modeling magnetohydrodynamic equilibrium we use a technique that is motivated by the finite element method [3]. First we develop a second order accurate numerical quadrature formula for the Hamiltonian E based on a rectangular grid of mesh points over a unit cube of the space with coordinates s, u and v.
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Due to its relative simplicity, finite-difference (FD) analysis was historically the first numerical technique for boundary value problems in mathematical physics.
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