<p>In order to accurately solve singularly perturbed two-point boundary value problems (BVPs) with an interior turning point, this paper proposes a robust numerical scheme built on a Shishkin mesh utilizing the trigonometric cubic <i>B</i>-spline (TCBS) approach. The considered problem exhibits two outflow-exponential boundary layers, making them challenging to approximate using standard numerical techniques. The proposed method efficiently captures the rapid variations within these layers while maintaining accuracy across the entire domain. A detailed convergence analysis confirms that the method attains an order of accuracy close to second order. Three benchmark numerical examples are provided to validate the theoretical results. The obtained numerical results indicate the method’s accuracy and show good agreement with the exact solution. Additionally, the effectiveness of the suggested method is compared with other numerical techniques that are currently available in the literature. The comparison indicates that the TCBS scheme yields highly accurate and stable results, even for small perturbation parameters.</p>