Efficient solution of differential equations by analytic continuation
- 21 August 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (12) , 2141-2149
- https://doi.org/10.1088/0305-4470/18/12/011
Abstract
A new method is described for the automatic solution of linear ordinary differential equations by the use of Taylor series. This new method is shown to be superior in speed and accuracy to conventional methods. The method is illustrated for Coulomb wavefunctions, confluent hypergeometric functions, zeros of Bessel functions and s-wave phaseshift for e-H scattering in the static approximation.Keywords
This publication has 9 references indexed in Scilit:
- Solving Ordinary Differential Equations Using Taylor SeriesACM Transactions on Mathematical Software, 1982
- High-precision evaluation of the regular and irregular Coulomb wavefunctionsJournal of Computational and Applied Mathematics, 1982
- Fast taylor-series expansion and the solution of the cauchy problemUSSR Computational Mathematics and Mathematical Physics, 1982
- Choosing a stepsize for Taylor series methods for solving ODE'SJournal of Computational and Applied Mathematics, 1977
- The automatic solution of systems of ordinary differential equations by the method of Taylor seriesThe Computer Journal, 1971
- Methods and applications of power seriesMathematics of Computation, 1966
- Algorithms 13: complex exponential integralCommunications of the ACM, 1960
- A Program for the Automatic Integration of Differential Equations using the Method of Taylor SeriesThe Computer Journal, 1960
- A NOTE ON THE NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONSThe Quarterly Journal of Mechanics and Applied Mathematics, 1949