Well-conditioned collocation schemes and new triangular spectral-element methods - Villena Samson, Michael Daniel (2014)
In the first portion of this thesis, a new well-conditioned collocation method for solving differential equations based on Birkhoff interpolation is presented. The collocation schemes on interior points using the interpolation basis functions produce linear systems that do not use differentiation matrices and have coefficient matrices with condition numbers independent of the number of points. The method is extended to different differentiation orders, computational domains