Numerical study of the Sturm–Liouville problem

Abstract

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.

Keywords

• sturm–liouville problem
• numerical algorithm without satura-tion
• computational experiment