spheroidal%20differential%20equation
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1—10 of 13 matching pages
1: Bibliography V
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Calculation of spheroidal wave functions.
J. Acoust. Soc. Amer. 51, pp. 414–416.
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Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials.
J. Comput. Appl. Math. 213 (2), pp. 488–500.
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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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2: Bibliography D
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Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations.
CWI Monographs, Vol. 2, North-Holland Publishing Co., Amsterdam.
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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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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point.
Anal. Appl. (Singap.) 12 (4), pp. 385–402.
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A survey on orthogonal matrix polynomials satisfying second order differential equations.
J. Comput. Appl. Math. 178 (1-2), pp. 169–190.
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3: 30.9 Asymptotic Approximations and Expansions
§30.9 Asymptotic Approximations and Expansions
►§30.9(i) Prolate Spheroidal Wave Functions
… ►§30.9(ii) Oblate Spheroidal Wave Functions
… ►§30.9(iii) Other Approximations and Expansions
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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation.
Adv. Quantum Chem. 72, pp. 95–127.
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The computation of eigenvalues and solutions of Mathieu’s differential equation for noninteger order.
ACM Trans. Math. Software 19 (3), pp. 377–390.
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Differential Equations with Applications and Historical Notes.
McGraw-Hill Book Co., New York.
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The linear differential equation whose solutions are the products of solutions of two given differential equations.
J. Math. Anal. Appl. 98 (1), pp. 130–147.
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Error bounds for asymptotic solutions of differential equations. I. The distinct eigenvalue case.
J. Res. Nat. Bur. Standards Sect. B 70B, pp. 167–186.
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5: Bibliography K
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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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Rational solutions of the fifth Painlevé equation.
Differential Integral Equations 7 (3-4), pp. 967–1000.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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On differential equations for Sobolev-type Laguerre polynomials.
Trans. Amer. Math. Soc. 350 (1), pp. 347–393.
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An algorithm for solving second order linear homogeneous differential equations.
J. Symbolic Comput. 2 (1), pp. 3–43.
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6: Bibliography L
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The two-point connection problem for differential equations of the Heun class.
Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).
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Some differential equations and associated integral equations.
Quart. J. Math. (Oxford) 5, pp. 81–97.
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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics.
J. Math. Phys. 27 (5), pp. 1238–1265.
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Computations of spheroidal harmonics with complex arguments: A review with an algorithm.
Phys. Rev. E 58 (5), pp. 6792–6806.
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The second Painlevé equation.
Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).
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7: Bibliography C
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Elementary Differential Equations.
Clarendon Press, Oxford.
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Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation.
Comm. ACM 12 (7), pp. 399–407.
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The numerical solution of linear differential equations in Chebyshev series.
Proc. Cambridge Philos. Soc. 53 (1), pp. 134–149.
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Theory of ordinary differential equations.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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8: Bibliography
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Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
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Algorithms for special integrals of ordinary differential equations.
J. Phys. A 29 (5), pp. 973–991.
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Periodic Differential Equations. An Introduction to Mathieu, Lamé, and Allied Functions.
International Series of Monographs in Pure and Applied
Mathematics, Vol. 66, Pergamon Press, The Macmillan Co., New York.
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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations.
Classics in Applied Mathematics, Vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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9: Bibliography B
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Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations.
The Macmillan Co., New York.
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Ordinary differential equations.
Fourth edition, John Wiley & Sons, Inc., New York.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods.
John Wiley & Sons Ltd., Chichester.
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Numerical Methods for Ordinary Differential Equations.
John Wiley & Sons Ltd., Chichester.
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