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… ►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. …
… ►There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …
§3.6 Linear Difference Equations… ►
§3.6(ii) Homogeneous Equations… ► … ► … ►
§3.6(iv) Inhomogeneous 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. …
… ►His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. …
… ►Her research interests include numerical grid generation, numerical solution of partial differential equations, and visualization of special functions. …
… ►For numerical solution of partial differential equations satisfied by the canonical integrals see Connor et al. (1983).
On the asymptotic and numerical solution of linear ordinary differential equations.
SIAM Rev. 40 (3), pp. 463–495.
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.
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.
Numerical solution of second-order linear difference equations.
J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
Numerical solution of Riemann-Hilbert problems: Painlevé II.
Found. Comput. Math. 11 (2), pp. 153–179.