Iteration method|Fixed point iteration method.

To find the real root of an equation f (x)=0 ...(1)
Which can be expressed in the form x=𝜙(x) ......(2)
First we find an initial approximate value x₀ for equation (1). The better approximation x₁ for the root is obtained by replacing x by x₀ in R.H.S of equation (2) i.e x₁ = 𝜙(x₀)
A still better approximation x₂ for the root is obtained by putting x=x₁ in the R.H.S of equation (2). Thus x₂ = 𝜙(x₁).
This procedure is continued and we get
x₃ = 𝜙(x₂)
x₄ = 𝜙(x₃)
.................
xₙ = 𝜙(xₙ₋₁)
If the sequence x₀,x₁,x₂,.......xₙ of approximate roots converges to a limit 𝛂, then 𝛂 is taken as the root of the equation f(x)=0.
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