Numerical approximation methods and their applications play an important role in many scientific and engineering fields. It enables us to solve mathematical equations that cannot be solved analytically, understand complex systems, and predict them. After the great development in mathematical modeling and programming, this role developed and grew. Since there are many vital applications, whether in engineering, physics, chemistry or economics, approximation methods combined with mathematical modeling have enabled us to solve complex problems that cannot be solved using only one method. Better understand and analyze complex systems, and solve complex problems. It also enables us to provide more accurate forecasts. The lenticular approximation method is based on dividing the problem into a series of small steps and then solving each step using simple analytical methods. Lenticular approximation methods can be divided into several types, including linear and nonlinear methods. In this study, this study aims to introduce the reader to numerical approximation methods in mathematical modeling. This study will discuss the types of numerical approximation methods and their applications in mathematical modeling. We studied a mathematical model and chose the appropriate method of approximation, then calculated the error rate and approximation error and verified the approximation. The results indicated that using numerical approximation methods and mathematical modeling together is a powerful tool that can be used to solve many complex problems and contributed to reducing the error rate by a very large percentage and reducing the standard deviation of the mathematical model.