central difference operator

central difference operator

[¦sen·trəl ¦dif·rəns ′äp·ə‚rād·ər]
(mathematics)
A difference operator, denoted ∂, defined by the equation ∂ƒ(x) = ƒ(x + h /2) - ƒ(x-h /2), where h is a constant denoting the difference between successive points of interpolation or calculation.
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Similarly, if we calculate the discrete problem of the left hand side equation in (3.2) using the same central difference operator by taking [[xi].sub.i] = [u.sup.2.sub.i], where u is the central difference computed solution for equation (2.1), we observe that LHS is negative wherever the solution is smooth enough and positive where we have boundary layers (or oscillation in the computed solution of equation (2.1)).
Recently, they [20] proposed a novel numerical method for the space Riesz fractional advection-dispersion equation based on fractional central difference operator. Ozdemir et al.
In [30], Tuan and Gorenflo introduced the following left fractional central difference operator:
As u(x, t) with respect to x belongs to [L.sub.1] (R), then the Fourier transform of the fractional average central difference operator (33) exists and has the following form:
uniformly holds for x [member of] R, where 8X denotes second-order central difference operator with respect to x and is defined by [[delta].sup.2.sub.x] u([x.sub.j], t) = u([x.sub.j + 1],t) - 2u([x.sub.j], t) + u([x.sub.j - 1], t).
In addition, users will be able to solve impact problems using either implicit (Newmark-beta operator) or explicit integration (central difference operator).

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