Numerical solution of second-order linear difference equations
TL;DR: In this paper, the authors describe a lion which is a ppli cable when s impl e rec urrence proce dures ca nnol be used becau se uf in sla bilil Y.
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Abstract: A ne w al~orilhm is ~ive n fur cumpulin ~ Ihe soluliun of a ny secu nd-orde r lin ea r diffe re nce e qua lion which is a ppli cable when s impl e rec urrence proce dures ca nnol be used becau 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 elhod has Ih e advanla~es of (i) a Ul umal ic ally deLermining the currec t number of rec urrence steps. (ii ) app lying to illllOlllo~en eou s differe nce eqlla ~ li uns, (iii ) e nab lin g mure powerful e rrur a na lyses lu be co ns lru c led. The me lhud is illuSlra led by num e rica l comp ulalion s, ineludin~ e rror ana lyses. uf A n~e rWe be r . S iruve, a nd Besse l fun c li uns, and Ih e s u luli un of a differe nli a l e qualiun in C he bys he v se ri es.
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Citations
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References
The numerical solution of linear differential equations in Chebyshev series
C. W. Clenshaw
- 01 Jan 1957
TL;DR: In this article, a method for computing the coefficients in the Chebyshev expansion of a solution of an ordinary linear differential equation is described. But the method is valid only when the solution required is bounded and possesses a finite number of maxima and minima in the finite range of integration.
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Error analysis of Miller’s recurrence algorithm
TL;DR: Strict upper bouinds are given for the errors in the values yielded by the algorithm, and general conclusions are drawn concerning the accuracy of the process.
47