Combined Compact Difference Scheme
Sixth order in the interior and thrid order at the boundaries.
Proposed by:
(1) "A Family of High Order Finite Difference Schemes with Good Spectral Resolution", Krishnan Mahesh, JCP 1998
(2) "A Three-Point Combined Compact Difference Scheme", Peter C.Chu and Chenwu Fan, JCP 1998
Matrix from:
(1) Page 6154, "Further improvement and analysis of CCD scheme: Dissipation discretization and de-aliasing properties", T.K.Sengupta, V.V.S.N.Vijay, S.Bhaumik, JCP 2009
(2) Page 356, "A Family of High Order Finite Difference Schemes with Good Spectral Resolution", Krishnan Mahesh, JCP 1998
Inverts the Matrix and finds x (of Ax=B) using Gauss Elimintaion (Code from Rosetta: https://rosettacode.org/wiki/Gaussian_elimination#Fortran)
Thanks to Dr.Sainath Chamarthi for the guidance!
Thanks to Prof.Tapan Sengupta and Dr.Aditi Sengupta for sending the references and for helping with the matrix.