Abstract:
We present the variational method for finding the eigenfunctions and eigenvalues in the Sturm–Liouville problem with Dirichlet boundary conditions; the method is based on the proposed functional. As a test example, we consider the potential $\cos(4x)$. Also computations for two functions $\sin((x-\pi)^2/\pi)$ and a high nonisosceles triangle are given.
Keywords:variational method, functional, Sturm–Liouville problem, eigenfunction, eigenvalue, Dirichlet boundary condition, the function $\sin((x-\pi)^2/\pi)$, the function $\cos(4x)$, nonisosceles triangle, random search method, Wolfram Research, “Nminimize” procedure, algorithm.
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