Continuous modelling
Encyclopedia
Continuous modelling is the mathematical practice of applying a model
to continuous
data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equation
s and are converse to discrete modelling
.
Modelling is generally broken down into several steps:
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 not only in the natural sciences and engineering disciplines A mathematical model is a...
to continuous
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s and are converse to discrete modelling
Discrete modelling
Discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, discrete formulae are fit to data. A common method in this form of modelling is to use recurrence relations....
.
Modelling is generally broken down into several steps:
- Making assumptions about the data: The modeller decides what is influencing the data and what can be safely ignored.
- Making equations to fit the assumptions.
- Solving the equations.
- Verifying the results: Various statistical tests are applied to the data and the model and compared.
- If the model passes the verification progress it is put into practice.