Here, we present a new algorithm that systematically solves the Taylor expansion coefficients problem for constructing implicit (compact) finite-difference schemes.
Although it is presented to construct up to 3rd-order differential compact schemes, we believe it is simple enough, so that users can easily extend it to obtain even higher-order schemes if necessary.
Also, we provide two examples:
The first example, demonstrates how to use the Taylor Table algorithm to recover well-known schemes in the literature. The second example, shows how to set a central compact scheme and complement it with suitable boundaries schemes. So that a (sparse) differential operator can be easily constructed ;)
Future work: In an expansion of these snippets I'll soon introduce a simple way to create 2D and 3D differential operators suitable for solving PDEs in Matlab ~stay tuned !
Happy coding !
Manuel A. Diaz (2021). Easy build compact schemes (https://www.mathworks.com/matlabcentral/fileexchange/90506-easy-build-compact-schemes), MATLAB Central File Exchange. Retrieved .
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