Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: A comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions

Journal of Computational Physics

Volumn 188, Issue 1, 2003, Pages 56-74

  Boyd, John P ^a   Rangan, C ^a   Bucksbaum, P H ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Coulomb; Eigenvalue; Laguerre; Mapped Fourier sine method; Quantum mechanics; Rational Chebyshev; Semi infinite interval

Indexed keywords

ATOMS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER SERIES; HYDROGEN; MAPPING; RATIONAL FUNCTIONS;

CHEBYSHEV; CHEBYSHEV FUNCTIONS; COULOMB; EIGEN-VALUE; FOURIER; LAGUERRE; MAPPED FOURIER-SINE METHOD; PSEUDOSPECTRAL METHODS; RATIONAL CHEBYSHEV; SEMI-INFINITE INTERVALS;

QUANTUM THEORY;

EID: 0038346445     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00127-X     Document Type: Article

References (26)

1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
2. K. Banerjee, Hermite function solution of quantum anharmonic oscillator, Proc. R. Soc. Lond. A 364 (1978) 264.
3. K. Banerjee, S.P. Bhatnagar, V. Choudhury, S.S. Kanwal, Anharmonic-oscillator, Proc. R. Soc. Lond. A 360 (1978) 575.
4. J.N. Bardsley, Case Stud. Atom. Phys. 4 (1974) 302.
5. A.G. Borisov, Solution of the radial Schrödinger equation in cylindrical and spherical coordinates by mapped Fourier transform algorithms, J. Chem. Phys. 114 (2001) 7770.
6. J.P. Boyd, Spectral and pseudospectral methods for eigenvalue and nonseparable boundary value problems, Mon. Weather Rev. 106 (1978) 1192.
7. J.P. Boyd, The choice of spectral functions on a sphere for boundary and eigenvalue problems: a comparison of Chebyshev, Fourier, and Associated expansions, Mon. Weather Rev. 106 (1978) 1184.
8. J.P. Boyd, The optimization of convergence for Chebyshev polynomial methods in an unbounded domain, J. Comp. Phys. 45 (1982) 43.
9. J.P. Boyd, Orthogonal rational functions on a semi-infinite interval, J. Comp. Phys. 70 (1987) 63.
10. J.P. Boyd, Spectral methods using rational basis functions on an infinite interval, J. Comp. Phys. 69 (1987) 112.
11. J.P. Boyd, Chebyshev domain truncation is inferior to Fourier domain truncation for solving problems on an infinite interval, J. Sci. Comp. 3 (1988) 109.
12. J.P. Boyd, The rate of convergence of Fourier coefficients for entire functions of infinite order with application to the Weideman-Cloot sinh-Mapping for pseudospectral computations on an infinite interval, J. Comp. Phys. 110 (1994) 360.
13. J.P. Boyd, Traps and snares in eigenvalue calculations with application to pseudospectral computations of ocean tides in a basin bounded by meridians, J. Comp. Phys. 126 (1996) 11; Corrigendum 136 (1997) 227.
14. J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, Mineola, NY, 2001.
15. A. Cloot, J.A.C. Weideman, Spectral methods and mappings for evolution equations on the infinite line, Comput. Meth. Appl. Mech. Eng. 80 (1990) 467.
16. A. Cloot, J.A.C. Weideman, An adaptive algorithm for spectral computations on unbounded domains, J. Comput. Phys. 102 (1992) 398.
17. P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, second ed., Academic Press, Boston, 1984.
18. A. Falqués, V. Iranzo, Edge waves on a longshore shear flow, Phys. Fluids 4 (1992) 2169.
19. E. Fattal, R. Baer, R. Kosloff, Phase space approach for optimizing grid representations: the mapped Fourier method, Phys. Rev. E 53 (1996) 1217.
20. H. Friedrich, Theoretical Atomic Physics, Springer, New York, 1990.
21. D. Lemoine, Optimized grid representations in curvilinear coordinates: the mapped sine Fourier method, Chem. Phys. Lett. 320 (2000) 492.
22. S.-H. Lin, R.T. Pierrehumbert, Does Ekman friction suppress baroclinic instability?, J. Atmos. Sci. 45 (1988) 2920.
23. M. Nest, H.-D. Meyer, Improving the mapping mechanism of the mapped Fourier method, Chem. Phys. Lett. 352 (2002) 486.
24. R.E. Robson, A. Prytz, The discrete ordinate/pseudo-spectral method: review and application from a physicist's perspective, Austral. J. Phys. 46 (1993) 465.
25. Tao Tang, The Hermite spectral method for Gaussian-type functions, SIAM J. Sci. Comput. 14 (1993) 594.
26. J.A.C. Weideman, S.C. Reddy, A MATLAB differentiation matrix suite, ACM Trans. Math. Software 26 (2000) 465.