Insights into Numerical Solution of First-order Growth Models using Hybrid Block Methods with Four Collocation Points

First-order growth models are fundamental in economics, finance, and various scientific disciplines for modeling dynamic processes. Solving these models numerically is often challenging due to their complex nature. Hybrid block methods have emerged as promising tools for efficiently and accurately solving such models. This article provides a comprehensive development, analysis and implementation of hybrid block method applied to the numerical solution of first-order growth models. We discuss the theoretical foundations, algorithmic implementations, and practical applications of these methods, highlighting their advantages and limitations. Additionally, we present numerical examples and comparisons with other numerical techniques to assess the performance of hybrid block method. Through these insights, we aim to provide insights into the state-of-the-art techniques for solving first-order growth models numerically.