An Algorithm for Computing Problems of Singular and Singularly Perturbed Types

This paper introduces the Hybrid Block Formula (HBF), an algorithm designed for computing problems of singular and singularly perturbed types. HBF utilizes numerical integration with Lagrange interpolation polynomial as the basis function, selecting integration limits strategically to navigate singularities smoothly. Theoretical analysis confirms HBF's zero-stability, consistency, and convergence. Application of HBF to various computing problems demonstrates its superiority in computational reliability and efficiency over comparative methods, as evidenced by numerical and graphical results.