Abstract
The complex zeros of solutions of second order linear ODEs lie over certain curves in the complex plane called anti-Stokes lines. We consider the Liouville-Green (WKB) approximation for linear homogeneous second order ODEs $$w^{\prime \prime }(z)+A(z)w(z)=0$$ with $$A(z)$$ meromorphic, and describe the qualitative properties of the approximate anti-Stokes lines. Based on this qualitative description, we construct a fourth order method which efficiently computes the complex zeros of solutions of second order ODEs following the path of the approximate anti-Stokes lines. We illustrate the method with the computation of the zeros of parabolic cylinder functions, Bessel functions and generalized Bessel polynomials and describe specific algorithms for the computation of these zeros.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
