Numerical Analysis of Equations: Methods, Accuracy, and Scientific Applications

One of the fundamental fields of applied mathematics is numerical analysis, which offers useful techniques for solving mathematical equations where an exact solution may not always exist. Algebraic equations, systems of linear equations, nonlinear equations, ordinary differential equations and partial differential equations are often used to model problems in science, engineering, economics, computer science and data analysis. Because often there is no exact analytical solution, numerical methods are used to approximate a solution with an error that can be controlled and a computational cost that is acceptable. Approximation, iterative algorithms, error analysis, stability, convergence and scientific applications of numerical analysis for the solution of equations are discussed. It also illustrates the need for selection of numerical methods with accuracy and efficiency. The article ends with a conclusion that numerical analysis is not just a computational method but a scientific analysis system to convert mathematical models into practical results