Liouville transformation for differential equations
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11—14 of 14 matching pages
11: 2.6 Distributional Methods
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§2.6(ii) Stieltjes Transform
… ►The Stieltjes transform of is defined by … ►Corresponding results for the generalized Stieltjes transform … ►The Riemann–Liouville fractional integral of order is defined by … ►For rigorous derivations of these results and also order estimates for , see Wong (1979) and Wong (1989, Chapter 6).12: 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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Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions.
Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
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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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13: 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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Algorithm 537: Characteristic values of Mathieu’s differential equation.
ACM Trans. Math. Software 5 (1), pp. 112–117.
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Some Differential Equations Satisfied by Hypergeometric Functions.
In Approximation and Computation (West Lafayette, IN, 1993),
Internat. Ser. Numer. Math., Vol. 119, pp. 371–381.
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The second Painlevé equation.
Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).
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14: 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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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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Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
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Special classes of solutions of Painlevé equations.
Differ. Uravn. 18 (3), pp. 419–429 (Russian).
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Theory of Painlevé’s equations.
Differ. Uravn. 11 (11), pp. 373–376 (Russian).
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