About the Project

spectral methods


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1: Daniel W. Lozier
Then he transferred to NIST (then known as the National Bureau of Standards), where he collaborated for several years with the Building and Fire Research Laboratory developing and applying finite-difference and spectral methods to differential equation models of fire growth. …
2: 18.39 Physical Applications
§18.39(i) Quantum Mechanics
3: 18.38 Mathematical Applications
This process has been generalized to spectral methods for solving partial differential equations. …
4: Bibliography G
  • J. S. Geronimo, O. Bruno, and W. Van Assche (2004) WKB and turning point theory for second-order difference equations. In Spectral Methods for Operators of Mathematical Physics, Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
  • D. Gottlieb and S. A. Orszag (1977) Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • B. Guo (1998) Spectral Methods and Their Applications. World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.
  • 5: Bibliography
  • J. C. Adams and P. N. Swarztrauber (1997) SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.
  • 6: 31.17 Physical Applications
    §31.17(i) Addition of Three Quantum Spins
    The problem of adding three quantum spins s , t , and u can be solved by the method of separation of variables, and the solution is given in terms of a product of two Heun functions. … Consider the following spectral problem on the sphere S 2 : x 2 = x s 2 + x t 2 + x u 2 = R 2 . … For more details about the method of separation of variables and relation to special functions see Olevskiĭ (1950), Kalnins et al. (1976), Miller (1977), and Kalnins (1986). … For applications of Heun’s equation and functions in astrophysics see Debosscher (1998) where different spectral problems for Heun’s equation are also considered. …
    7: Brian D. Sleeman
    Sleeman has published numerous papers in applied analysis, multiparameter spectral theory, direct and inverse scattering theory, and mathematical medicine. He is author of the book Multiparameter spectral theory in Hilbert space, published by Pitman in 1978, and coauthor (with D. … Sleeman was elected a Fellow of the Royal Society of Edinburgh in 1976 and is founding editor of the journal Computational and Mathematical Methods in Medicine. …
    8: Bibliography M
  • A. J. MacLeod (1996b) Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.
  • P. L. Marston (1992) Geometrical and Catastrophe Optics Methods in Scattering. In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.), Vol. 21, pp. 1–234.
  • J. M. McNamee (2007) Numerical Methods for Roots of Polynomials. Part I. Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.
  • V. Meden and K. Schönhammer (1992) Spectral functions for the Tomonaga-Luttinger model. Phys. Rev. B 46 (24), pp. 15753–15760.
  • S. L. B. Moshier (1989) Methods and Programs for Mathematical Functions. Ellis Horwood Ltd., Chichester.
  • 9: Bibliography K
  • D. K. Kahaner, C. Moler, and S. Nash (1989) Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..
  • J. P. Keating (1999) Periodic Orbits, Spectral Statistics, and the Riemann Zeros. In Supersymmetry and Trace Formulae: Chaos and Disorder, J. P. Keating, D. E. Khmelnitskii, and I. V. Lerner (Eds.), pp. 1–15.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • M. K. Kerimov (1999) The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.
  • A. D. Kerr (1978) An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.
  • 10: 31.8 Solutions via Quadratures
    ϵ = - m 3 + 1 2 , m 0 , m 1 , m 2 , m 3 = 0 , 1 , 2 , ,
    the Hermite–Darboux method (see Whittaker and Watson (1927, pp. 570–572)) can be applied to construct solutions of (31.2.1) expressed in quadratures, as follows. … The variables λ and ν are two coordinates of the associated hyperelliptic (spectral) curve Γ : ν 2 = j = 1 2 g + 1 ( λ - λ j ) . …