Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation

Abstract

A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented, which depend on different engineering applications. The method is found to have a truncation error of O(h6) and converges to the exact solution at O(h4). The numerical examples show that our method is very effective and the maximum absolute error is acceptable. Keywords: Self-adjoint singularly-perturbation problems, Two-point boundary value problems, Trigonometric quintic B-spline collocation method, MSC: 41A15, 65M70, 65M12, 65L11