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While the great laminar regularity of inter-areal projection patterns is certainly intriguing, it remains open for discussion whether elaborate schemes for ordering brain areas hierarchically are fundamentally helpful for understanding cortical organization (Hegdé and Felleman 2007; Markov et al. 2013).
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Variants of the Monotone Upstream-centred Scheme for Conservation Laws and Weighted Essentially Non-Oscillatory schemes for orders of accuracy ranging from second to ninth order, as well as with and without low Mach corrections, have been investigated.
Figure 2 Plot of upper and lower solutions of coupled system of Example 2. By the use of a monotone iterative technique, we successfully developed a scheme for order upper and lower solutions to the coupled system of highly nonlinear fractional order differential equations with coupled integral boundary conditions.
Each of these four schemes for second-order derivatives requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables.
The finite difference schemes for constant-order time or space fractional diffusion equations have been widely studied [14 19].
The finite difference schemes for constant-order time or space fractional diffusion equations have been widely studied [21, 22].
We build a simple and general class of finite difference schemes for first order Hamilton Jacobi (HJ) Partial Differential Equations.
The finite difference schemes for constant-order time or space fractional diffusion equations have been extensively considered in the literature; see, for instance, the work done in [14 19].
Such operations are characteristic to our motivating application in PyFR an implementation of Flux Reconstruction schemes for high-order fluid flow simulations on mixed unstructured meshes.
The use of NSFD schemes for fractional-order problems is a quite new subject and very few contributions are available in literature [32 34].
Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators.
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