# Welcome to Numerical Methods in C’s Tutorials !¶

Iterative Solutions to Non Linear Equations:

In this unit we shall discuss 5 methods for solutions of non linear simulataneous equation namely-
• Fixed Point Iteration
• Bisection Method
• Regula Falsi Method
• Newton Raphson Method
• Secant Method

First thing first, well all the codes illustrated in this tutorial are tested and compiled on a linux machine. To compile a C code, fire up a terminal by CTRL+ALT+T and type

gcc -o test test.c


where test.c is the name of program we want to compile. To execute a program

./test


Disclaimer: Well Please refer to a standard Text Book for detailed coverage of Theory, In this tutorial only minimal theoretical information will be put up which is essential for understanding the working of the method.

So, lets dive in...

Non-linear Equations is a set of equations in which unknowns appear as variables of a polynomial of degree higher than one. Examples are

$\begin{split}x^2 = 25 \\y^2-y=6\\x^2-sinx=1\end{split}$

These powers and vaiables may get complicated in that case, In that case manual hand computation will be too troublesome, so we can use numerical techniques to do the computations on computers and get results.

A computer code trying to solve a particular problem should have these characterstics properly specified

(1) Algorithm or Method Formula
There are two type of Methods
+-------------------------------+
|                               |
Iterative Methods               Direct Methods

(2) Stopping Condition: In case of Iterative methods we get closer
to actual solution in each iteration,
so we may need to define a sufficient and necessary
condition which will stop further iterations and prints the
results in desired accuracy.


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