The main contents of numerical analysis include numerical solutions of algebraic equations, linear algebraic equations and differential equations, numerical approximation of functions, solution of matrix eigenvalues, optimization calculation, probability and statistics calculation, and theoretical problems such as existence, uniqueness, convergence and error analysis of solutions.

The main research directions of numerical analysis include numerical functional analysis and complexity theory of continuous calculation, numerical differentiation and finite element, nonlinear numerical algebra and complex dynamic system, numerical solution of nonlinear equations, numerical approximation theory, computer simulation and information processing, and mathematical modeling and calculation of engineering problems.

Characteristics of numerical analysis

Applied mathematics: Applied mathematics is the general name of mathematical theories and methods with clear application purposes. Studying how to apply mathematical knowledge to other branches of mathematics (especially science) can be said to be the opposite of pure mathematics. Graph theory is applied to network analysis, and number theory is applied to cryptography, game theory, probability theory, statistics and economics, all of which show the application of mathematics in different categories.

Bio-mathematics: Computational mathematics mainly studies calculation methods related to various scientific and engineering calculations, conducts theoretical and numerical analysis on various algorithms and their applications, designs and studies numerical simulation methods to replace some expensive and even difficult experiments, and studies special or general scientific and engineering application software and numerical software.