second-order
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11—20 of 41 matching pages
11: Bibliography W
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Asymptotic expansions for second-order linear difference equations with a turning point.
Numer. Math. 94 (1), pp. 147–194.
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Asymptotic expansions for second-order linear difference equations. II.
Stud. Appl. Math. 87 (4), pp. 289–324.
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Asymptotic expansions for second-order linear difference equations.
J. Comput. Appl. Math. 41 (1-2), pp. 65–94.
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12: 15.11 Riemann’s Differential Equation
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►The importance of (15.10.1) is that any homogeneous linear differential equation of the second order with at most three distinct singularities, all regular, in the extended plane can be transformed into (15.10.1).
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►The reduction of a general homogeneous linear differential equation of the second order with at most three regular singularities to the hypergeometric differential equation is given by
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13: Bibliography Z
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Error bounds for asymptotic solutions of second-order linear difference equations.
J. Comput. Appl. Math. 71 (2), pp. 191–212.
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14: 10.72 Mathematical Applications
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►Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter.
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15: 33.23 Methods of Computation
16: 3.8 Nonlinear Equations
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►This is useful when satisfies a second-order linear differential equation because of the ease of computing .
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►For describing the distribution of complex zeros of solutions of linear homogeneous second-order differential equations by methods based on the Liouville–Green (WKB) approximation, see Segura (2013).
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17: 18.36 Miscellaneous Polynomials
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►Classes of such polynomials have been found that generalize the classical OP’s in the sense that they satisfy second order matrix differential equations with coefficients independent of the degree.
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►The satisfy a second order Sturm–Liouville eigenvalue problem of the type illustrated in Table 18.8.1, as satisfied by classical OP’s, but now with rational, rather than polynomial coefficients:
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18: Bibliography N
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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole.
Ph.D. Thesis, University of Maryland, College Park, MD.
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19: 31.16 Mathematical Applications
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► thesis “Inversion problem for a second-order linear differential equation with four singular points”.
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20: Bibliography G
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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 the zeros and turning points of solutions of second order homogeneous linear ODEs.
SIAM J. Numer. Anal. 41 (3), pp. 827–855.
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