Cardinal Pseudospectral method for solving the periodic and semiperiodic Sturm-Liouville problem

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55136-553, Maragheh, Iran.

2 Department of Mathematics, Instute for Advanced Studies in Basic Sciences, (IASBS), Zanjan, 45137-66731, Iran.

10.22034/cmde.2026.70632.3522

Abstract

This paper investigates the periodic and semiperiodic Sturm--Liouville problem. We begin by examining the fundamental properties of its eigenvalues and eigenfunctions. In the first part, the eigenvalues are approximated utilizing the pseudospectral method using the Chebyshev cardinal functions. While existing literature predominantly focuses on numerical and theoretical analysis of the eigenvalues, this study, in its second part, shifts focus to the eigenfunctions themselves. For both periodic and semiperiodic cases, we demonstrate that the explicit computation of these eigenfunctions is achievable. The methodology involves formulating the problem into the Volterra integral equation, which is then solved numerically via the pseudospectral method. Finally, the numerical results are rigorously validated by comparing them with analytical solutions. Error terms at both the inception and termination of the interval are calculated and bench marked against exact results, confirming the accuracy and efficacy of the proposed method.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 19 February 2026

Files

History

  • Receive Date: 08 December 2025
  • Revise Date: 04 February 2026
  • Accept Date: 17 February 2026

Share

How to cite

Statistics