Since the publication of qSpectral Methods in Fluid Dynamicsq 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.Now (5.5.23) follows using (5.5.9) and (5.6.23). ... They are the eigenfunctions of the singular Sturm-Liouville problem (2.2.1) where p(x) = (1 a x)Ip+1(1 + x)I²+1 (Ip and I² agt; a1), q(x) ai 0 and w(x) = (1 a x)Ip(1 + x)I². ... Furthermore, Jacobi polynomials enter into the construction 5.7 Other Polynomial Approximations 309 CIX CX.
|Author||:||Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, Thomas A. Zang|
|Publisher||:||Springer Science & Business Media - 2007-09-23|