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This work aims to provide approximate solutions for singularly perturbed problems with periodic boundary conditions using quintic B-splines and collocation. The well-known Shishkin mesh strategy is applied for mesh construction. Convergence analysis demonstrates that the method achieves parameter-uniform convergence with fourth-order accuracy in the maximum norm. Numerical examples are presented to validate the theoretical estimates. Additionally, the standard hybrid finite difference scheme, a cubic spline scheme, and the proposed method are compared to demonstrate the effectiveness of the present approach.

Details

1009240
Subject
Boundary conditions;
Mathematical functions;
Approximation;
Singular perturbation;
Methods;
Finite element analysis;
Convergence;
Mathematical analysis;
Finite difference method;
Boundary value problems;
Collocation methods
Identifier / keyword
singular perturbation; periodical boundary conditions; parameter-uniform convergence; collocation points; quintic B-splines
Title
A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems
Author
Arumugam, Puvaneswari 1   VIAFID ORCID Logo  ; Thynesh, Valanarasu 2   VIAFID ORCID Logo  ; Muthusamy, Chandru 3   VIAFID ORCID Logo  ; Ramos, Higinio 4   VIAFID ORCID Logo 

1  Department of Mathematics, University College of Engineering, Anna University, Tiruchirappalli 620024, Tamilnadu, India; [email protected] 
2  Department of Mathematics, CDOE, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India; [email protected] 
3  Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India; [email protected] 
4  Department of Applied Mathematics, Scientific Computing Group, University of Salamanca, Plaza de la Merced, 37008 Salamanca, Spain 
Publication title
Axioms; Basel
Volume
14
Issue
1
First page
73
Publication year
2025
Publication date
2025
Publisher
MDPI AG
Place of publication
Basel
Country of publication
Switzerland
Publication subject
Mathematics
e-ISSN
20751680
Source type
Scholarly Journal
Language of publication
English
Document type
Journal Article
Publication history
 
 
Online publication date
2025-01-20
Milestone dates
2024-11-28 (Received); 2025-01-15 (Accepted)
Publication history
 
 
   First posting date
20 Jan 2025
DOI
https://doi.org/10.3390/axioms14010073
ProQuest document ID
3159327377
Document URL
https://www.proquest.com/scholarly-journals/quintic-spline-based-computational-method-solving/docview/3159327377/se-2?accountid=208611
Copyright
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2025-01-24
Database
ProQuest One Academic