An introduction to Numerical Techniques

An introduction to Numerical Techniques

Mathematics is an elegant and precise subject.  However when numerical answers are required one sometimes needs to rely on approximate methods to obtain useable answers.

There are many problems which simply do not have analytical solutions, or those whose exact solution is beyond our current state of knowledge. There are also many problems which are too long (or tedious) to solve by hand. When such problems arise we can exploit numerical analysis to reduce the problem to one involving a finite number of unknowns and use a computer to solve the resulting equations.

The text starts with a description of how we could perform some very basic calculations (that is, simply using the computer as a calculator). It then moves on to solving problems which cannot, in practice, be solved by hand.

Sometimes the solution of these problems can become as intricate and involved as the original problems and requires almost as much finesse and care to obtain a solution. There are several options available to us, both in terms of language and also overall approach.

Finding roots of non-linear equations

An standard equation, y=f(x)………………………(1)

Equation (1) may be of any kind of following equations:

1.     Algebraic Equation

2.    Polynomial equation

3.    Transcendental equations

Linear eqn: y=3x + 5

Non-linear equation: y= x^2 +1

                                 2x+3xy-25=0

Methods of solution:

1.     Direct methods

2.    Graphical methods

3.    Trial and error methods

4.    Iterative methods