Sentence examples for by central difference approximation from inspiring English sources
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.
end{aligned} (35) For (i=M), substitution of the approximate unknown value of the right boundary by a traditional central difference approximation [23] with the known derivative the right boundary condition gives C_{M+1}^{n} = C_{M-1}^{n} + 2Delta x S_{0}.
By using a central difference approximation, curvature mode shapes were then calculated from the displacement mode shapes.
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.
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).
When compared with the four-point central difference approximation method, the calculation of two-point difference approximation method is very simple.
The convergence behavior of our method is consistent with that of the central difference approximation of the classical Laplace operator.
Let L ij denote a central difference approximation to the operator ∂ x i ( d i j ∂ x j ).
The central difference approximation of L ll, (l = 1, 2) guarantees that it is diagonally dominant tri-diagonal.
Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered.
