Variational Estimation Methods for Sturm–Liouville Problems

In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (...

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Bibliographic Details
Main Authors: Elena Corina Cipu, Cosmin Dănuţ Barbu
Format: Article
Language:English
Published: MDPI AG 2022-10-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/10/20/3728
Description
Summary:In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (the variational equation associated through the Euler–Lagrange variational principle and Nehari’s method, shooting method and bisection method) and iterative variational methods (He’s method and HPM) for regular RSL are unitary presented in final part of the paper, which ends with applications.
ISSN:2227-7390