A note on Olver’s algorithm for the solution of second-order linear difference equations

Cash, J. R.

doi:10.1090/S0025-5718-1980-0572854-5

Mathematics of Computation

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A note on Olver’s algorithm for the solution of second-order linear difference equations
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by J. R. Cash PDF

Math. Comp. 35 (1980), 767-772 Request permission

Abstract:

An extension of Olver’s algorithm is described. This allows the solution of certain linear difference equations which are in a sense ill-conditioned for solution by Olver’s method. The new algorithm is illustrated by considering a particular problem.

References

Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 10.1137/1009002
F. W. J. Olver, Numerical solution of second-order linear difference equations, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 111–129. MR 221789, DOI 10.6028/jres.071B.018
J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422