numerical study of the sturm–liouville problem

The article discusses the general sturm–liouville problem. to solve it numerically, a new algorithm is proposed, which is based on the varia-tional principle and does not use saturation. the problem of constructing numerical methods for solving eigenvalue problems can be divided into two stages. first, we need to reduce the infinite-dimensional problem into a finite-dimensional one, and then find a method for solving this finite-dimensional algebraic eigenvalue problem. in this paper, we only consider the first stage, and solve the resulting algebraic problem using the qr al-gorithm. a comparison with the results of other authors is also carried out. methodical calculations confirm the correctness of the new approach.