Investigation of the Basic Notions in Numerical Analysis (original) (raw)

Numerical analysis plays a crucial role in modeling complex real-world phenomena through mathematical frameworks that often lead to the need for numerical methods due to challenges in obtaining analytical solutions. This investigation focuses on the transformation of continuous mathematical models into discrete numerical models while ensuring no significant loss of information occurs. The study emphasizes the importance of ensuring that the discrete problems are well-posed and computationally efficient, explores the key concepts of consistency and stability, and articulates their relationship to convergence in numerical modeling.