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Zbl 1056.65049
Gil, Amparo; Segura, Javier
Computing the zeros and turning points of solutions of second order homogeneous linear ODEs. (English)
[J] SIAM J. Numer. Anal. 41, No. 3, 827-855 (2003). ISSN 0036-1429; ISSN 1095-7170/e

The authors present two algorithms for computing the zeros and turning points of solutions of second order ordinary differential equations (ODEs). Both algorithm rely on fixed point methods. The first one is based on the first-order systems associated with a set of second order ODEs, whilst for the second method the fixed point iterations stem from the second order ODEs. Moreover, it is shown that both methods are quadratically convergent. \par The efficiency of these methods as well as the combined methods is illustrated by different examples. Comparison with other algorithms is also provided.
[Z. Jackiewicz (Tempe)]

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)
65L05 Initial value problems for ODE (numerical methods)
33F05 Numerical approximation of special functions
34A34 Nonlinear ODE and systems, general

Keywords: second-order ODEs; zeros and turning points; special functions; numerical examples; algorithms; fixed point methods; fixed point iterations

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