Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in the social sciences (such as economics, psychology, sociology, political science).

A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.

Elements of a mathematical model

Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.

In the physical sciences, a traditional mathematical model contains most of the following elements:

  1. Governing equations
  2. Supplementary sub-models
    1. Defining equations
    2. Constitutive equations
  3. Assumptions and constraints
    1. Initial and boundary conditions
    2. Classical constraints and kinematic equations
Other Languages
العربية: نموذج رياضي
한국어: 수학적 모델
Bahasa Indonesia: Model matematika
Nederlands: Wiskundig model
日本語: 数理モデル
norsk nynorsk: Matematisk modell
oʻzbekcha/ўзбекча: Matematik model
Simple English: Mathematical model
slovenčina: Matematický model
српски / srpski: Математички модел
srpskohrvatski / српскохрватски: Matematički model
Tiếng Việt: Mô hình toán học
中文: 数学模型