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(2) Tradition forward-backward diffusion models are often implemented by finite difference scheme or multi-grid technique whose computing efficiency is always low in practice.
As a first example, we consider the couple ({f,g }), where u a,t)=f(t)=chi_{[1,2]}, and (g(t)=u(b,t)) is computed by finite difference scheme (see Section 2.2).
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This equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws.
It is known that the numerical solutions calculated by finite difference schemes are always associated with numerical dissipation and dispersion.
We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes.
In this paper, highly absorbing and stable boundary conditions for linear partial differential equations discretized by finite difference schemes are directly designed using a flexible, optimization-based formulation.
The development is based on the use of the motion equation which is discretized by finite difference schemes approximating spatial derivatives of the displacement.
With a coarse grid cast over the whole domain and the coarse scale dynamics computed by finite difference schemes, we perform a fast average of the fine scale solution in the atomistic subdomain to force agreement between scales.
The system of governing equations is solved by a finite difference scheme.
The transformed boundary layer equations are solved numerically by a finite difference scheme, namely the Keller-box method.
The procedure is based on the minimization of the difference between the profiles calculated by a finite difference scheme and the experimental profiles.
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