A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems - Puvaneswari Arumugam; Valanarasu Thynesh; Chandru Muthusamy; Higinio Ramos (Axioms)
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.