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inhomogeneous differential equations

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1: 1.13 Differential Equations
§1.13(iii) Inhomogeneous Equations
Variation of Parameters
2: 11.13 Methods of Computation
A comprehensive approach is to integrate the defining inhomogeneous differential equations (11.2.7) and (11.2.9) numerically, using methods described in §3.7. …
3: 3.7 Ordinary Differential Equations
If h = 0 the differential equation is homogeneous, otherwise it is inhomogeneous. … … The latter is especially useful if the endpoint b of 𝒫 is at , or if the differential equation is inhomogeneous. …
4: 11.9 Lommel Functions
The inhomogeneous Bessel differential equationFor uniform asymptotic expansions, for large ν and fixed μ = 1 , 0 , 1 , 2 , , of solutions of the inhomogeneous modified Bessel differential equation that corresponds to (11.9.1) see Olver (1997b, pp. 388–390). …
5: Bibliography O
  • A. B. Olde Daalhuis (2004b) On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation. J. Comput. Appl. Math. 169 (1), pp. 235–246.
  • 6: 2.8 Differential Equations with a Parameter
    For error bounds, extensions to pure imaginary or complex u , an extension to inhomogeneous differential equations, and examples, see Olver (1997b, Chapter 10). …
    7: 11.10 Anger–Weber Functions
    The Anger and Weber functions satisfy the inhomogeneous Bessel differential equation
    8: 11.2 Definitions
    §11.2(ii) Differential Equations
    9: 9.12 Scorer Functions
    9.12.20 Hi ( z ) = 1 π 0 exp ( 1 3 t 3 + z t ) d t ,
    9.12.30 0 z Gi ( t ) d t 1 π ln z + 2 γ + ln 3 3 π 1 π k = 1 ( 3 k 1 ) ! k ! ( 3 z 3 ) k , | ph z | 1 3 π δ .
    9.12.31 0 z Hi ( t ) d t 1 π ln z + 2 γ + ln 3 3 π + 1 π k = 1 ( 1 ) k 1 ( 3 k 1 ) ! k ! ( 3 z 3 ) k , | ph z | 2 3 π δ ,
    10: Bibliography L
  • V. Laĭ (1994) The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).
  • C. G. Lambe and D. R. Ward (1934) Some differential equations and associated integral equations. Quart. J. Math. (Oxford) 5, pp. 81–97.
  • W. R. Leeb (1979) Algorithm 537: Characteristic values of Mathieu’s differential equation. ACM Trans. Math. Software 5 (1), pp. 112–117.
  • J. Letessier, G. Valent, and J. Wimp (1994) Some Differential Equations Satisfied by Hypergeometric Functions. In Approximation and Computation (West Lafayette, IN, 1993), Internat. Ser. Numer. Math., Vol. 119, pp. 371–381.
  • N. A. Lukaševič (1971) The second Painlevé equation. Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).