second order
(0.003 seconds)
11—20 of 149 matching pages
11: 10.75 Tables
12: 22.13 Derivatives and Differential Equations
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§22.13(iii) Second-Order Differential Equations
…13: Bibliography E
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The Fuchsian equation of second order with four singularities.
Duke Math. J. 9 (1), pp. 48–58.
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On the transformation theory of ordinary second-order linear symmetric differential expressions.
Czechoslovak Math. J. 32(107) (2), pp. 275–306.
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14: 2.9 Difference Equations
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►or equivalently the second-order homogeneous linear difference equation
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►This situation is analogous to second-order homogeneous linear differential equations with an irregular singularity of rank 1 at infinity (§2.7(ii)).
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►For asymptotic approximations to solutions of second-order difference equations analogous to the Liouville–Green (WKBJ) approximation for differential equations (§2.7(iii)) see Spigler and Vianello (1992, 1997) and Spigler et al. (1999).
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►For discussions of turning points, transition points, and uniform asymptotic expansions for solutions of linear difference equations of the second order see Wang and Wong (2003, 2005).
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15: 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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16: 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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17: 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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18: 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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19: 33.23 Methods of Computation
20: 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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