8/10/2019 Significance of Numerical Methods

1/3

Numerical methods are techniques by which mathematical problems are

formulated so that they can be solved with arithmetic operations. While numerical

methods can be divided into many types, all of them have one thing in common: a

large quantity of long arithmetic calculations.

Apart from numerical methods, the other two methods of problem solving

are analytical methods and graphical methods. The latter isn't useful since it isn't

precise due to the drawing of graphs using hands. This also makes the process

tedious. Another limitation is its viability for problems involving three or lesser

dimensions. Usage of analytical methods can give one insight into the behavior

and characteristics of a particular system. Unfortunately, they can only be used for

systems which can be approximated through use of linear models. Since practical

problems consist of complex and nonlinear processes, the use of analytical

methods isn't adequate.

Historically, analytical and graphical methods were preferred due to the time

consuming nature of numerical methods highlighted above. Multiple arithmetic

operations consumed a lot of time since the only tools in hand were slide rules,

calculators and paper and pencil. The number of operations also increased the

chance of a wrong outcome due to a human blunder.

The introduction and explosive spread of affordable computers in the

modern era has changed the perception about numerical methods and altered the

ways of problem solving. A computer is able to perform millions of calculations in

a second. Thus the speed bottleneck associated with numerical methods has been

removed.

8/10/2019 Significance of Numerical Methods

2/3

Numerical methods are quite significant in the field of engineering since

they allow us to learn in-depth knowledge about the various systems in the

multiple streams of engineering. This is possible since it prioritizes the right

stages of problem solving. There are three stages of problem solving in

engineering practice:

Formulation

Solution

Interpretation

While analytical methods focus on the solution stage ( in order to come up with a

simplified model to output an answer), the techniques applied in numerical

methods focus on the formulation and interpretation stages. The formulation

stage consists of finding the best relationship between the dimensions of the

problem and the fundamental laws of nature. Since computing power has

transformed the solution stage into a time efficient stage, importance is placed on

formulation stage in order to come up with the best possible answer. Numerical

methods also open up more possibilities in the interpretation stage. Due to ease

in calculations, the mathematical model setup in the formulation stage can be

easily tweaked repeatedly in order to understand more about the characteristics

of the system in question. Types of such tweaks:

Larger Systems:

More dimensions/components added into the mathematical model. This makes

the system more realistic.

8/10/2019 Significance of Numerical Methods

3/3

Non ideal systems:

Usually systems are solved for ideal conditions. The model can be reformulated to

include nonidealised realities present in a practical problem.

Sensitivity Analysis:

Implementation of computational numerical methods allows one to test the

system for different inputs in order to determine the sensitivity of the system.

Tasks which tend to be quite common to be solved using numerical methods are:

Finding roots

Solving linear equations

Numerical Interpolation

Calculus

Numerical methods are used in nearly every stream of engineering:

Kinematics

Temperature distribution

Circuitry