An extension of Olver's method for the numerical solution of linear recurrence relations

Author:
J. R. Cash

Journal:
Math. Comp. **32** (1978), 497-510

MSC:
Primary 65Q05

DOI:
https://doi.org/10.1090/S0025-5718-1978-0483578-8

MathSciNet review:
0483578

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Abstract: An algorithm is developed for computing the solution of a class of linear recurrence relations of order greater than two when unstable error propagation prevents the required solution being found by direct forward recurrence. By abandoning an appropriate number of initial conditions the original problem may be replaced by an inexact but well-conditioned boundary value problem, and in certain circumstances the solution of this new problem is a good approximation to the required solution of the original problem. The required solution of this reposed problem is generated using an algorithm based on Gaussian elimination, and a technique developed by Olver is extended to estimate automatically the truncation error of the proposed algorithm.

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0483578-8

Article copyright:
© Copyright 1978
American Mathematical Society