1. Calculation function method: Using various numerical methods to solve the second-order differential equation can quickly solve the problems of qualitative and stability methods.
2. Lagrange difference equation method: finite difference step comparison method is used to solve qualitative and stability methods, thus helping users to quickly understand the system behavior.
3. High-order difference method: A group of high-order difference equations are used to describe the stability model in an accurate high-order approximate form, which effectively solves the qualitative and stability problems.
Extended data
Qualitative and Stability Methods of Ordinary Differential Equations is a textbook for master students and senior undergraduates majoring in applied mathematics. It mainly includes qualitative theory, stability theory and bifurcation theory. Focusing on the needs of application, the content is concise, focusing on revealing the essence of concepts, expounding theorem ideas, introducing application methods and analyzing examples, and introducing computer software that meets the content. There are exercises at the end of this chapter.
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.
Including differential equation, vector analysis, matrix, Fourier transform, complex variable analysis, numerical method, probability theory, mathematical statistics, operational research, control theory, combinatorial mathematics, information theory and many other branches of mathematics, including the study of mathematical problems raised from various application fields. Computational mathematics can sometimes be regarded as a part of applied mathematics.
Applied mathematics contains two words: "application" and "mathematics". Generally speaking, applied mathematics consists of two parts. One part is mathematics related to application, which is a branch of traditional mathematics. We can call it "applied mathematics". The other part is the application of mathematics, that is, using mathematics as a tool to explore and solve problems in science, engineering and sociology, which is beyond the scope of traditional mathematics.
2 1 century, applied mathematics is mainly applied in two fields. One is a computer. With the rapid development of computer, a large number of software engineers who understand mathematics are needed to develop the corresponding database. The other is economics, many of which need very professional mathematics to analyze. Many related courses of applied mathematics are designed on the basis of economic examples.