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The explicit group methods use small fixed group formulations derived from a combination of the rotated five-point finite difference approximation together with the centered five-point centered difference approximation on different grid spacings.
It should be noted that we can use the non-centered difference instead of the centered difference (8).
We discretize the system via centered difference approximations.
We determine the error of the Riesz fractional derivative to the fractional centered difference.
The resulting symplectic and space centered difference scheme renders an optimized numerical dispersion relation equation.
First, the centered difference approach is used to approximate the Riesz fractional derivative in space.
Similar(29)
The methodology is a linear and implicit technique which is based on fractional centered differences.
To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences.
We furthermore observe that it is essential to use the adaptive multiresolution method, which mixes centered differences with TVD methods.
A spectral-like viscosity is proposed for centered differencing schemes to help stabilize numerical solutions and reduce oscillations near discontinuities.
We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity.
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