Computational study demonstrates an algorithm for unstable second-order linear difference equations, indicating improved step determination and error control over Miller's method.
A ne w a l~orilhm is ~ive n fur c umpulin ~ Ih e soluliun of a n y secu nd-ord e r lin ea r diffe re nce e qu a li on which is a ppli c able when s impl e rec urrence proc e dures ca nnol be u se d bec au se uf in sla bilil Y. Co mpare d wilh Ih e we ll -knuwn lV1ill e r a l ~o rilhm Ih e ne w m e lhod has Ih e advanla~es of (i) a Ul umal ic ally d eLe rminin g th e currec t number of rec urre nce st eps. (ii ) app lying to illllOlllo ~e n eo u s diffe re nce e qlla ~ li uns, (iii ) e nab lin g mure powerful e rrur a n a lyses lu be co ns lru c le d.
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F. W. J. Olver (1967) studied this question.
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