Spectral method for differential equations of degenerate type on unbounded domains by using generalized Laguerre functions

Applied Numerical Mathematics

Volumn 57, Issue 4, 2007, Pages 455-471

  Guo, Ben yu ^a   Zhang, Xiao yong ^b  

^a SHANGHAI NORMAL UNIVERSITY   (China)

^b SHANGHAI MARITIME UNIVERSITY   (China)

Author keywords

Orthogonal approximation by using generalized Laguerre functions; Partial differential equations of degenerate type; Spectral method for unbounded domains

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; SPECTRUM ANALYSIS;

FINANCIAL MATHEMATICS; GENERALIZED LAGUERRE FUNCTIONS; ORTHOGONAL APPROXIMATION; PARTIAL DIFFERENTIAL EQUATIONS OF DEGENERATE TYPE; SPECTRAL METHOD FOR UNBOUNDED DOMAINS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33847309675     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.07.032     Document Type: Article

References (24)

1. Bergh J., and Löström J. Interpolation Spaces, An Introduction (1976), Springer, Berlin
2. Black F., and Scholes M. The pricing of options and corporate liabilities. J. Political Economy 81 (1973) 637-654
3. Black F., Derman E., and Toy W. A one factor model of interest rates and its application to treasury bond options. Financial Analysts J. 46 (1990) 33-39
4. Cox J.C., Ingersoll J.E., and Ross S.A. A theory of the term structure of interest rates. Econometrica 53 (1985) 385-407
5. Dothan L.U. On the term structure of interest rates. J. Financial Economics 6 (1978) 59-69
6. Funaro D. Polynomial Approximations of Differential Equations (1992), Springer, Berlin
7. Guo B.-y., and Ma H.-p. Composite Legendre-Laguerre approximation in unbounded domains. J. Comp. Math. 19 (2001) 101-112
8. Guo B.-y., and Jie S. Error estimates of Laguerre spectral approximation for Benjamin-Bona-Mahony equation on the half line. Numer. Math. 86 (2000) 635-654
9. Guo B.-y., Jie S., and Xu C.-l. Generalized Laguerre approximation and its applications to exterior problems. J. Comp. Math. 23 (2005) 113-130
10. Guo B.-y., Wang L.-l., and Wang Z.-q. Generalized Laguerre interpolation and pseudospectral method for unbounded domain. SIAM J. Numer. Anal. 43 (2006) 2567-2589
11. Guo B.-y., and Xu C.-l. Mixed Laguerre-Legendre pseudospectral method for incompressible flow in an infinite strip. Math. Comp. 72 (2003) 95-125
12. Guo B.-y., and Zhang X.-y. A new generalized Laguerre approximation and its applications. J. Comp. Appl. Math. 181 (2005) 342-363
13. Ben-yu Guo, Xiao-yong Zhang, Spectral method for three-dimensional nonlinear Klein-Gordon equation by using generalized Laguerre and spherical harmonic functions, submitted for publication
14. Hardy G.H., Littlewood J.E., and Pólya G. Inequalities (1952), Cambridge University Press, Cambridge
15. Iranzo V., and Falquès A. Some spectral approximations for differential equations in unbounded domains. Comput. Methods Appl. Mech. Engrg. 98 (1992) 105-126
16. Maday Y., Pernaud-Thomas B., and Vanderen H. Reappraisal of Laguerre type spectral methods. La Recherche Aerospatiale 6 (1985) 13-35
17. Oleinik A., and Radkevic E. Second Order Equations with Nonnegative Characteristic Form (1973), AMS/Plenum Press, Rhode Island/New York
18. Jie S. Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM Numer. Anal. 38 (2002) 1113-1133
19. Wilmott P., Howison S., and Dewynne J. Option Pricing: Mathematical Models and Computation (1993), Oxford Financial Press, Oxford
20. Windcliff H., Forsyth P.A., and Vetzal K.R. Analysis of the stability of the linear boundary condition for the Black-Scholes equation. J. Comp. Fin. 8 (2004) 65-92
21. Cheng-long Xu, Laguerre spectral-finite difference method for a class of degenerated PDEs in finance, J. Comp. Appl. Math., submitted for publication
22. Xu C.-l., and Guo B.-y. Laguerre pseudospectral method for nonlinear partial differential equations. J. Comp. Math. 20 (2002) 77-96
23. Xu C.-l., and Guo B.-y. Mixed Laguerre-Legendre spectral method for incompressible flow in an infinite strip. Adv. Comp. Math. 16 (2002) 77-96
24. Zhang X.-y., and Guo B.-y. Spherical harmonic-generalized Laguerre spectral method for exterior problem. J. Sci. Comp. 27 (2006) 523-537