Numerical Analysis
Finding a Root Of a Function Using Sequence!
Why Do Is It Even Exist?
You can try & solve this equation using a calculator but it would only give you an inaccurate result x^2 - 742x + 2 = 0
It's mainly used by engineers who aim for the fastest & easiest answer of a solution regardless the method used.
How Can You Apply One Of The Methods?
Iterative Method:
1.Put x in one side& the other side of the equation on the side
2. Denote x (of the highest power) ---> n+1 & other x ---> n
3.Approximate the root of the equation from the graph
4.Let x1= *approximated root* & insert it in the equation
5.Keep repeating the process until you reach the level of accuracy needed !
Simple Example To Clear The Idea
Consider the function:
x^3 -3x +1=0
x^3 +1=3x
x^3 +1=3x
x=(1/3)(x^3 +1)
x *n+1* = (1/3)(x*n*^3 +1)
I approximated the 1st root to be 0.5-----> x1 = 0.5
x2 = (1/3)(x1^3 +1)=(1/3)(0.53 +1)= 0.375...
x3 = (1/3)(x2^3 +1)=(1/3)(0.3753 +1)= 0.3509…
x4 = (1/3)(x3^3 +1)=(1/3)(0.35093 +1)= 0.3477…
x5 = (1/3)(x4^3 +1)=(1/3)(0.34773 +1)= 0.3473…
It' Uses
Civil Engineering
Structural analysis. Traffic simulations. Environmental simulation. Geographic information system and GPS & So on
Chemical Engineering
Molecular modeling. System simulation bio medical engineering & so on
Computer & Communication Engineering
Network analysis. Signal processing. Electromagnetic fields.