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A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems

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Pubblicato in:Axioms vol. 14, no. 1 (2025), p. 73
Autore principale: Arumugam, Puvaneswari
Altri autori: Thynesh, Valanarasu, Muthusamy, Chandru, Ramos, Higinio
Pubblicazione:
MDPI AG
Soggetti:
Boundary conditions
Mathematical functions
Approximation
Singular perturbation
Methods
Finite element analysis
Convergence
Mathematical analysis
Finite difference method
Boundary value problems
Collocation methods
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Abstract: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.
ISSN:2075-1680
DOI:10.3390/axioms14010073
Fonte:Engineering Database