Computing the zeros and turning points of solutions of second order homogeneous linear ODEs.

*(English)*Zbl 1056.65049The 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.

The efficiency of these methods as well as the combined methods is illustrated by different examples. Comparison with other algorithms is also provided.

Reviewer: Z. Jackiewicz (Tempe)

##### MSC:

65H05 | Single nonlinear equations (numerical methods) |

65L05 | Initial value problems for ODE (numerical methods) |

33F05 | Numerical approximation and evaluation of special functions |

34A34 | Nonlinear ODE and systems, general |