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
