Abstract
This research paper introduces a new block method to solve third-order boundary-value problems (BVPs) directly. The method uses a suitable polynomial and three intermediate points to approximate the theoretical solution of third-order BVPs. An approximate solution is provided within the integration interval, and the basic properties of the proposed method, including convergence and stability, are theoretically analyzed. To assess the effectiveness of the proposed method, several real-life problems, such as boundary layer problems and physical model problems, are solved numerically. After comparison with some existing methods, the results of numerical experiments confirm the practical utility and effectiveness of the proposed method in real-world applications by demonstrating that it is superior and highly efficient in performance.