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Mathematics of Computation

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An algorithm for nondominant solutions of linear second-order inhomogeneous difference equations

Authors: Takemitsu Hasegawa and Tatsuo Torii
Journal: Math. Comp. 64 (1995), 1199-1214
MSC: Primary 65Q05; Secondary 65F05
MathSciNet review: 1284668
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Abstract: An algorithm is given for computing a weighted sum of a nondominant solution of a linear second-order inhomogeneous difference equation to a prescribed accuracy by estimating the truncation error. The present method is an extension of both the stable numerical method due to Olver and Sookne and a summation technique due to Deuflhard for computing minimal solutions of a homogeneous difference equation. The method is illustrated by numerical examples.

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Keywords: Three-term recurrence relation, nondominant solution, numerical instability, LU factorization, rank-one updating
Article copyright: © Copyright 1995 American Mathematical Society