Mathematical Modelling
Mathematical modelling is the process of
constructing mathematical
objects
whose
behaviors or properties correspond in some ways to a particular real-world
system. In
this description, a mathematical object could be a system of
equations, a stochastic process, a geometric or algebraic structure, an
algorithm, or even just a set of numbers. The term real-world
system refers
to a physical system, a biological system, a social system, an
ecological system, or essentially any other system whose behaviors can
be
observed. In
fact, once a physical system has been observed and phenomenologically
analyzed, it is often useful to use mathematical models suitable to
describe
its evolution both in time and space. Indeed, the interpretations of
systems
and phenomena, which occasionally show complex features, are generally
developed on the basis of methods which organize their interpretations
toward
simulation. When simulations related to the behavior of the real system
are
available and reliable, it may be possible, in most cases, to reduce
time
devoted to observations and experiments.
Many
specific
reasons
are there for developing the mathematical modelling,
but most
are related in some ways to the following two steps.
- To gain understanding. Generally speaking, if we have a mathematical model which accurately reflects some behavior of a real-world system of interest, we can often gain improved understanding of that system through analysis of the model. Furthermore, in the process of building the model we find out which factors are most important in the system, and how different parts of the system are related.
- To predict or simulate. Very often we wish to know what a real-world system will do in the future, but it is expensive, impractical, or impossible to experiment directly with the system. Examples include nuclear reactor design, space light, extinction of species, weather prediction, hyperthermia and drug efficacy in human bodies, and so on.
Faculty Involved : K N Rai,
S Das, SK Pandey