Solving an inverse nodal problem with Herglotz-Nevanlinna functions in boundary conditions using the second-kind Chebyshev wavelets method

Abstract

This study considers Sturm-Liouville (S-L) equation with a special function which includes spectral parameter at boundary conditions and expresses asymptotic forms of inverse problem solution, nodal points, and lengths. Furthermore, it proves some uniqueness theorems. Doing this, approximate solution of inverse S-L problem is obtained by second-kind Chebyshev polynomials whereby the second-kind Chebyshev wavelets (SCW) method is used to solve these types of problems. Finally, effectiveness of the method is demonstrated in a few examples.