UAT tension B-spline collocation method for solving a class of singularly perturbed convection-diffusion problems

Abstract

In this paper, we introduce a novel collocation method that utilizes Uniform Algebraic Trigonometric (UAT) tension B-splines to resolve a class of convection-diffusion problems with singular perturbations on a Shishkin mesh. We provide a rigorous analysis of the method's uniform convergence in relation to the perturbation parameter. To demonstrate the efficacy of the proposed approach, we conduct numerical experiments and compare the results with various benchmark problems from the literature. The findings highlight the accuracy and effectiveness of our method in addressing such problems.