ordinary differential equations
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1: 9.15 Mathematical Applications
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►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point.
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2: 32.17 Methods of Computation
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►The Painlevé equations can be integrated by Runge–Kutta methods for ordinary differential equations; see §3.7(v), Hairer et al. (2000), and Butcher (2003).
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3: 3.7 Ordinary Differential Equations
§3.7 Ordinary Differential Equations
… ►For an introduction to numerical methods for ordinary differential equations, see Ascher and Petzold (1998), Hairer et al. (1993), and Iserles (1996). … ►§3.7(iv) Sturm–Liouville Eigenvalue Problems
… ►§3.7(v) Runge–Kutta Method
… ►An extensive literature exists on the numerical solution of ordinary differential equations by Runge–Kutta, multistep, or other methods. …4: Bibliography O
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Exponentially improved asymptotic solutions of ordinary differential equations. II Irregular singularities of rank one.
Proc. Roy. Soc. London Ser. A 445, pp. 39–56.
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On the asymptotic and numerical solution of linear ordinary differential equations.
SIAM Rev. 40 (3), pp. 463–495.
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On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation.
J. Comput. Appl. Math. 169 (1), pp. 235–246.
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Exponentially-improved asymptotic solutions of ordinary differential equations I: The confluent hypergeometric function.
SIAM J. Math. Anal. 24 (3), pp. 756–767.
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Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank unity.
Methods Appl. Anal. 4 (4), pp. 375–403.
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5: Bibliography H
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Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.
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Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer-Verlag, Berlin.
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Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.
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Ordinary Differential Equations in the Complex Domain.
Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.
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6: Bibliography I
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Ordinary Differential Equations.
Longmans, Green and Co., London.
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7: Bibliography D
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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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Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions.
Stud. Appl. Math. 113 (3), pp. 245–270.
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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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8: Bibliography
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Algorithms for special integrals of ordinary differential equations.
J. Phys. A 29 (5), pp. 973–991.
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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 J
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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II.
Phys. D 2 (3), pp. 407–448.
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