Computation of eigenfunctions and eigenvalues for the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint

A functional-based variational method is proposed for finding the eigenfunctions and eigenvalues in the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint. Computations are performed for three potentials: $\sin((x-\pi)^2/\pi)$, $\cos(4x)$, and a high nonisosceles triangle.