A numerical method for evaluating zeros of solutions of second-order linear differential equations
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- by Renato Spigler and Marco Vianello PDF
- Math. Comp. 55 (1990), 591-612 Request permission
Abstract:
A numerical algorithm for computing real zeros of solutions of 2nd-order linear differential equations $y”+ q(x)y = 0$ in the oscillatory case on a half line is studied. The method applies to the class $q(x) = a + b/x + O({x^{ - p}})$, with $a > 0$, $b \in {\mathbf {R}}$, $p > 1$. 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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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