Quasi-Lp norm orthogonal Galerkin expansions in sums of Jacobi polynomials: Orthogonal expansions

Numerical Algorithms

Volumn 54, Issue 4, 2010, Pages 533-569

  Livermore, Philip W ^a,b   Ierley, Glenn R ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Exponential convergence; Galerkin expansion; Jacobi polynomial; Orthogonal polynomial; Spectral method

Indexed keywords

EID: 77954456665     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-009-9353-5     Document Type: Article

References (17)

1. Askey, R.: Orthogonal Polynomials and Special Functions. SIAM, Philadelphia (1975).
2. Andrews, G. E., Burge, W. H.: Determinant identities. Pac. J. Math. 158, 1-14 (1993).
3. Boyd, J. P.: Chebyshev and Fourier Spectral Methods. Dover, New York (2001).
4. Doha, E. H., Bhrawy, A. H.: A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations. Numer. Methods Partial Differ. Equ. 25(3) (2009).
5. Golub, G. H., van Loan, C. F.: Matrix Computations, third edn. Johns Hopkins, Baltimore (1996).
6. Gosper, R. W., Jr.: Decision procedure for indefinite hypergeometric summation. Proc. Natl. Acad. Sci. USA 75, 40-42 (1977).
7. Ierley, G. R.: A class of sparse spectral operators for inversion of powers of the Laplacian in N dimensions. J. Sci. Comp. 12, 57-73 (1997).
8. Ierley, G. R., Kerswell, R. R., Plasting, S. C.: Infinite Prandtl number convection. Part 2: a singular limit of upper bound theory. J. Fluid Mech. 560, 159-227 (2005).
9. Ismail, M.: Classical and quantum orthogonal polynomials in one variable. In: Encyclopedia of Mathematics and its Applications, vol. 98. CUP (2005).
10. Koekoek, R., Swarttouw, R. F.: The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Delft University of Technology, Faculty of Information Technology and Systems, Department of Technical Mathematics and Informatics, Report no. 98-17 (1998).
11. Livermore, P.: Galerkin orthogonal polynomials. J. Comp. Phys. (2009, in press).
12. Livermore, P.: A compendium of Galerkin orthogonal polynomials. Tech. Rep., Scripps Institution of Oceanography, UC San Diego. Available at http://escholarship. org/uc/item/9vk1c6cm.
13. Luke, Y.: The Special Functions and Their Approximations, vol. 1, first edn. Academic, London (1969).
14. Marcellan, F., Ronveaux, A.: On a class of polynomials orthogonal with respect to a discrete Sobolev inner product. Indag. Math., N. S. 1(4), 451-464 (1990).
15. Mason, J. C., Handscomb, D. C.: Chebyshev Polynomials. Chapman & Hall, London (2003).
16. Szegö, G.: Orthogonal Polynomials, fourth edn. American Mathematical Society, Providence (1975).
17. Weber, M., Erdelyi, A.: On the finite difference analogue of Rodrigues' formula. Am. Math. Mon. 59, 163-168 (1952).