finite_difference

Computes finite difference matrices for the first and second derivative up to sixth order, including compact finite-difference schemes such as the fourth-order Padé scheme and sixth-order Lele scheme (S. K. Lele. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103(1):16–42, November 1992).

Methods available

• 2nd order
• 4th order
• 6th order
• Padé (4th order compact scheme)
• Lele (6th order compact scheme)

Examples

Example 1 - derivatives_example.py

This example is to demonstrate the perfomance of the different methods available. The function used in this example is given by:

which has the following derivatives:

Relative error (in log scale) obtained for the first derivative:

Relative error (in log scale) obtained for the second derivative:

Example 2 - 2D_first_derivatives_example.py

The function shown in the example files is given by:

The partial derivatives are given by:

The images below show the absolute error in log scale for both the partial derivatives in x and y direction.

Second order

Fourth order

Sixth order

Padé fourth order

Lele sixth order