A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems
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-un...
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MDPI AG
2025-01-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/1/73 |
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| author | Puvaneswari Arumugam Valanarasu Thynesh Chandru Muthusamy Higinio Ramos |
| author_facet | Puvaneswari Arumugam Valanarasu Thynesh Chandru Muthusamy Higinio Ramos |
| author_sort | Puvaneswari Arumugam |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-78d3b8a91c6944af9b757d1585766f07 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-78d3b8a91c6944af9b757d1585766f072025-01-24T13:22:20ZengMDPI AGAxioms2075-16802025-01-011417310.3390/axioms14010073A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value ProblemsPuvaneswari Arumugam0Valanarasu Thynesh1Chandru Muthusamy2Higinio Ramos3Department of Mathematics, University College of Engineering, Anna University, Tiruchirappalli 620024, Tamilnadu, IndiaDepartment of Mathematics, CDOE, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, IndiaDepartment of Applied Mathematics, Scientific Computing Group, University of Salamanca, Plaza de la Merced, 37008 Salamanca, SpainThis 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.https://www.mdpi.com/2075-1680/14/1/73singular perturbationperiodical boundary conditionsparameter-uniform convergencecollocation pointsquintic B-splines |
| spellingShingle | Puvaneswari Arumugam Valanarasu Thynesh Chandru Muthusamy Higinio Ramos A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems Axioms 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 |
| title_full | A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems |
| title_fullStr | A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems |
| title_full_unstemmed | A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems |
| title_short | A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems |
| title_sort | quintic spline based computational method for solving singularly perturbed periodic boundary value problems |
| topic | singular perturbation periodical boundary conditions parameter-uniform convergence collocation points quintic B-splines |
| url | https://www.mdpi.com/2075-1680/14/1/73 |
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