differentiator_type Derived Type

public pure function diff_periodic(self, f, dx) result(df)

Apply a differentiation stencil along a one dimensional pencil, assuming periodic boundaries. For instance, with a four point stencil $s = (-2, -1, 1, 2)$ and weights ${g_{i}}_{1 \leq i \leq 4}$

$$g(1) = g_1f_{n-2} + g_2f_{n-1} + g_3f_{2} + g_4f_{3}$$ $$g(2) = g_1f_{n-1} + g_2f_{1} + g_3f_{3} + g_4f_{4}$$

$$g(i) = g_1f_{i-2} + g_2f_{i-1} + g_3f_{i+1} + g_4f_{i+2}, i = 3, n-2$$

$$g(n-1) = g_1f_{n-3} + g_2f_{n-2} + g_3f_{n} + g_4f_{2}$$ $$g(n) = g_1f_{n-2} + g_2f_{n-1} + g_3f_{2} + g_4f_{3}$$

Arguments

Return Value real, allocatable, (:)

Derivative, evaluated on pencil