Performance Evaluation of a computational Block Method For Solving Quadratic Riccati Differential Equations: A Numerical Validation and Comparative analysis

Abstract

This study presents a computational block method derived through interpolation and collocation using power series polynomials for solving quadratic Riccati differential equations (QRDEs). A rigorous analysis of the method's core properties including order, consistency, and stability confirms its theoretical soundness. The method's performance was evaluated by applying it to three benchmark QRDEs. Numerical results demonstrate that the proposed method achieves significantly higher accuracy compared to several existing techniques documented in the literature. The study concludes that the computational block method is an efficient and reliable numerical tool for solving QRDEs, offering superior precision and convergence characteristics.