Abstract
Miller's recurrence algorithm for tabulating the subdominant solution of a second-order difference equation is modified so as to take the asymptotic behaviour of the solution into account. The asymptotic solutions of various types of equations are listed, and a method is given for estimating the error in the tabulated solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
British Association for the Advancement of Science,Bessel function — Part II, Mathematical Tables, Vol. 10; Cambridge University Press (1952).
F. W. J. Olver,Error analysis of Miller's recurrence algorithm, Math. Comp. 18 (1964), 65.
F. W. J. Olver,Numerical solution of second-order linear difference equations, J. Res. N. B. S. 71B (1967), 111.
F. W. J. Olver,Bounds for the solution of second-order linear difference equations, J. Res. N.B.S. 71B (1967), 161.
J. Oliver,Relative error propagation in the recursive solution of linear recurrence relations, Num. Math. 9 (1967), 323.
J. Oliver,The numerical solution of linear recurrence relations, Num. Math. 11 (1968), 349.
J. Oliver,An extension of Olver's error estimation technique for linear recurrence relations, Num. Math. 12 (1968), 459.
W. Gautschi,Recursive computation of repeated integrals of the error function, Math. Comp. 15 (1961), 227.
W. Gautschi,Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24.
H. Shintani,Note on Miller's recurrence algorithm, J. Sci. Hiroshima Univ. Ser. A-I 29 (1965), 121.
R. E. Scraton,A procedure for summing asymptotic series, Proc. Edin. Math. Soc. 16 (1969), 317.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scraton, R.E. A modification of Miller's recurrence algorithm. BIT 12, 242–251 (1972). https://doi.org/10.1007/BF01932818
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01932818