Derivative-Free Broyden's Method for Inverse Partially Known Sturm-Liouville Potential Functions

Athassawat Kammanee

Abstract

In this research a general potential function is recovered by  the information of not only a set of equispaced nodes on half its domain but also a sequence of given eigenvalues. Furthermore in each iteration step Numerov's method is the main tool used to approximate  the eigenvalues.
In order to achieve  our aim derivative-free Broyden's method is applied to
solve a system of nonlinear equations. Additionally, the numerical implementation demonstrates that our method provides agreeable results.