.PDE.MOL.SpaceDerivative.Derivatives.u_x

Information

The u_x block computes the first-order space derivative. By using the Newton-Gregory backward polynomial we
obtain

If we wish a second-order central difference approximation, we need to fit the polynomial through the three points
x_i-1, x_i, x_i+1. This means to write the polynomial for example around the point x_i+1, drop the higher-oder terms and set s = -1 to obtain

where h = x_i+1 - x_i (for i = 0,..., n-1). We assume here that the grid points are spaced equally.
For the boundary point x₁ we use biased formula and obtain

By using the same idea we obtain a biased formula for the boundary point x_n

Release Notes:

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