For the discretization of the Riemann-Liouville fractional derivative, we use the definition in (4 - 5) and replace the second-order space derivatives by central difference approximation.
Under environmental conditions of T : 10 ≤ T ≤ 30 °C, P : 60 ≤ P ≤ 120 kPa, and H : 5 ≤ H ≤ 85 %, we confirmed the accuracy of the two-point central difference approximation method via numerical calculations.
The gradient term ∇ a E, for example, can then be approximated using the central difference approximation as ∇ aE ≈ E ( Φ a, b, h, θ ) − E ( Φ a − ϵ, b, h, θ ) 2 ϵ. (16).
We determined that the GRA computation can be easily approximated by the two-point central difference approximation method and that approximation accuracies of less than 5 × 10− 9 can be achieved over the entire wavelength range (301.5-1698.5 nm) with Δλ = 1.5 nm and 12-digit PRA accuracy.
In addition [23], we found that the GRA computation can be easily approximated by the four-point central difference approximation method and that approximation accuracies of less than 30 × 10− 9 can be achieved over the entire wavelength range (320-1680 nm) with a step size of 10 nm.
It has been discovered that although central difference approximations are locally second-order accurate, they often suffer from computational instability and the resulting solutions exhibit non-physical oscillations.
By using a central difference approximation, curvature mode shapes were then calculated from the displacement mode shapes.
The convergence behavior of our method is consistent with that of the central difference approximation of the classical Laplace operator.
Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered.
After reviewing concisely the basic concepts relevant to the FORM, the central difference approximation is subsequently introduced to estimate the partial derivatives of the LSF.
In this study an explicit central difference approximation of the generalized leap-frog type is applied to the one- and two-dimensional advection equations.
