Numerical solution of second-order linear difference equations

Abstract

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 m-pare 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. The me lhud is illu Slra le d by num e ri ca l comp ulalion s, ineludin~ e rror ana lyses. uf A n ~e r-W e b e r. S iruv e, a nd Besse l fun c li un s, and Ih e s u luli un of a differe nli a l e qualiun in C he bys he v se ri es. Key Word s: C h e b ys he v se ri es, diffe re nce equa l ion s. e rrur anal ys is. Mil le r a lgor ililln. rec urre nce m e l huds. s pecia l fu nc l iu n s .