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1: 18.40 Methods of Computation
Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree. …
2: 16.25 Methods of Computation
There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …
3: 3.6 Linear Difference Equations
§3.6 Linear Difference Equations
§3.6(ii) Homogeneous Equations
§3.6(iv) Inhomogeneous Equations
4: 3.7 Ordinary Differential Equations
§3.7(ii) Taylor-Series Method: Initial-Value Problems
§3.7(iii) Taylor-Series Method: Boundary-Value 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. …
5: Ronald F. Boisvert
His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. …
6: Bonita V. Saunders
Her research interests include numerical grid generation, numerical solution of partial differential equations, and visualization of special functions. …
7: 36.15 Methods of Computation
For numerical solution of partial differential equations satisfied by the canonical integrals see Connor et al. (1983).
8: Bibliography O
  • A. B. Olde Daalhuis and F. W. J. Olver (1998) On the asymptotic and numerical solution of linear ordinary differential equations. SIAM Rev. 40 (3), pp. 463–495.
  • F. W. J. Olver and F. Stenger (1965) Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 244–249.
  • F. W. J. Olver (1965) On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 225–243.
  • F. W. J. Olver (1967a) Numerical solution of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
  • S. Olver (2011) Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.
  • 9: 18.38 Mathematical Applications
    Differential Equations
    10: 14.21 Definitions and Basic Properties
    §14.21(ii) Numerically Satisfactory Solutions
    When ν - 1 2 and μ 0 , a numerically satisfactory pair of solutions of (14.21.1) in the half-plane | ph z | 1 2 π is given by P ν - μ ( z ) and Q ν μ ( z ) . …