A numerical method for evaluating zeros of solutions of second-order linear differential equations

Authors:
Renato Spigler and Marco Vianello

Journal:
Math. Comp. **55** (1990), 591-612

MSC:
Primary 65L99; Secondary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035945-7

MathSciNet review:
1035945

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Abstract | References | Similar Articles | Additional Information

Abstract: A numerical algorithm for computing real zeros of solutions of 2nd-order linear differential equations in the oscillatory case on a half line is studied. The method applies to the class , with , , .

This procedure is based on a certain nonlinear 3rd-order equation (Kummer's equation) which plays a role in the theory of transformations of 2nd-order differential equations into each other, and was earlier introduced by F. W. J. Olver in 1950 to compute zeros of cylinder functions. A rigorous asymptotic and numerical analysis is developed by combining Borůvka's approach to the study of Kummer's equation *and* Olver's original idea. Numerical examples are presented.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1990-1035945-7

Keywords:
Ordinary differential equations,
zeros of functions,
asymptotic and numerical approximation of zeros,
special functions

Article copyright:
© Copyright 1990
American Mathematical Society