spectral solutions
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11—20 of 20 matching pages
11: Bibliography R
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Composite approximations to the solutions of the Orr-Sommerfeld equation.
Studies in Appl. Math. 51, pp. 341–368.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow.
Studies in Appl. Math. 53, pp. 91–110.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory.
Studies in Appl. Math. 53, pp. 217–224.
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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (4), pp. 91.
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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (3), pp. 56–64.
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12: Bibliography K
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Determinant structure of the rational solutions for the Painlevé II equation.
J. Math. Phys. 37 (9), pp. 4693–4704.
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Determinant structure of the rational solutions for the Painlevé IV equation.
J. Phys. A 31 (10), pp. 2431–2446.
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Asymptotic behavior of the solutions of the Painlevé equation of the first kind.
Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).
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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.
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Asymptotic solution of Maxwell’s equations near caustics.
Izv. Vuz. Radiofiz. 7, pp. 1049–1056.
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13: 18.39 Applications in the Physical Sciences
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►The solutions of (18.39.8) are subject to boundary conditions at and .
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►The solutions (18.39.8) are called the stationary states as separation of variables in (18.39.9) yields solutions of form
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►Brief mention of non-unit normalized solutions in the case of mixed spectra appear, but as these solutions are not OP’s details appear elsewhere, as referenced.
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►The radial Coulomb wave functions
, solutions of
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►Shizgal (2015) gives a broad overview of techniques and applications of spectral and pseudo-spectral methods to problems arising in theoretical chemistry, chemical kinetics, transport theory, and astrophysics.
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14: Bibliography H
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High frequency solutions of the delta wing equations.
Proc. Roy. Soc. Edinburgh Sect. A 81 (3-4), pp. 299–316.
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Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems.
Ph.D. Thesis, Technischen Universität Berlin.
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Solutions of Poisson’s equation in channel-like geometries.
Comput. Phys. Comm. 115 (1), pp. 45–68.
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Two Parametric Eigenvalue Problems of Differential Equations.
In Spectral Theory of Differential Operators (Birmingham, AL,
1981),
North-Holland Math. Stud., Vol. 55, pp. 233–241.
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15: Bibliography G
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The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals.
Ann. of Math. (2) 48 (4), pp. 785–826.
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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.
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Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments.
ACM Trans. Math. Software 30 (2), pp. 145–158.
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Numerical Analysis of Spectral Methods: Theory and Applications.
Society for Industrial and Applied Mathematics, Philadelphia, PA.
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Spectral Methods and Their Applications.
World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.
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16: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►A survey is given of the formal spectral theory of second order differential operators, typical results being presented in §1.18(i) through §1.18(viii).
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►One then needs a self-adjoint extension of a symmetric operator to carry out its spectral theory in a mathematically rigorous manner.
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►Spectral expansions of , and of functions of , these being expansions of and in terms of the eigenvalues and eigenfunctions summed over the spectrum, then follow:
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►Then, for , iff is an ordinary solution (i.
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Spectral expansions and self-adjoint extensions
…17: Bibliography E
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Ten Physical Applications of Spectral Zeta Functions.
Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.
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Certain expansions of solutions of the Heun equation.
Quart. J. Math., Oxford Ser. 15, pp. 62–69.
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The Sobolev orthogonality and spectral analysis of the Laguerre polynomials for positive integers
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J. Comput. Appl. Math. 171 (1-2), pp. 199–234.
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18: Bibliography P
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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations.
J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.
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Numerical Solution of Sturm-Liouville Problems.
Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.
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19: Bibliography D
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Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes.
Phys. Rev. E (3) 57 (1), pp. 252–275.
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Pole dynamics for elliptic solutions of the Korteweg-de Vries equation.
Math. Phys. Anal. Geom. 3 (1), pp. 49–74.
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Linear operators. Part II.
Wiley Classics Library, John Wiley & Sons, Inc., New York.
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Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one.
Methods Appl. Anal. 3 (1), pp. 109–134.
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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions.
Stud. Appl. Math. 107 (3), pp. 293–323.
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20: Bibliography M
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The 192 solutions of the Heun equation.
Math. Comp. 76 (258), pp. 811–843.
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Rational solutions of the Painlevé VI equation.
J. Phys. A 34 (11), pp. 2281–2294.
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Picard and Chazy solutions to the Painlevé VI equation.
Math. Ann. 321 (1), pp. 157–195.
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Spectral functions for the Tomonaga-Luttinger model.
Phys. Rev. B 46 (24), pp. 15753–15760.
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Classical solutions of the third Painlevé equation.
Nagoya Math. J. 139, pp. 37–65.
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