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+# Example 12     Chapter 6       Page no.: 162
+# Fixed point method Convergence and Divergence
+
+# Installing and importing package 'spuRs'
+install.packages("spuRs")
+library("spuRs")
+
+#Given function when converted in terms of 'x'
+f <- function(x){
+  5/x
+}
+cat("Let initial value be 1")
+x0 <- 1
+
+F1 <- fixedpoint(f,x0)
+cat("This type of divergence is called OSCILLATORY DIVERGENCE")
+
+cat(" Let us assume another function x=(x^2)+x-5")
+f1 <- function(x){
+  (x^2)+x-5
+}
+cat("Let initial value be 0")
+x0 <- 0
+F2 <- fixedpoint(f1,x0)
+
+cat("This type of divergence is called MONOTONE DIVERGENCE as it diverges rapidly")
+
+#*********************************************
+
+# Error May occour when calculating convergence on f1.
+# It is due to rapid divergance.
+
+#*********************************************
+
+cat(" Let us assume another function 2x=(5/x)+x")
+f3 <- function(x){
+  (x+(5/x))/2
+}
+cat("Let initial value be 1")
+x0 <- 1
+F3 <- fixedpoint(f3,x0)
+
+cat("This time the function converges rapidly")
+cat("The square root of 5 is",signif(F3,digits = 5))
+
+