1 files changed, 53 insertions, 0 deletions
diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.10/Ex13_10.R b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.10/Ex13_10.R
new file mode 100644
index 00000000..320eae02
--- /dev/null
+++ b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.10/Ex13_10.R
@@ -0,0 +1,53 @@
+# Example 10     Chapter 13       Page no.: 446
+# Milne-Simpson predictor-corrector method
+
+#for the solution 
+cat(" Milne and Simpson method")
+h <- 0.25
+y <- c()
+x <- c()
+x[1] = 1
+y[1] = 2
+
+cat("h=",h)
+cat("x=",x)
+cat("y=",y)
+
+f <- function(x,y){
+  2 * y / x
+}
+
+#Creating algorithm and displaying
+for (i in 2:10) {
+  
+  print(signif(y[i-1],3))
+  m1 <- f(x[i-1],y[i-1])
+  m2 <- f(x[i-1] + 0.5*h, y[i-1] + 0.5*h*m1)
+  m3 <- f(x[i-1] + 0.5*h, y[i-1] + 0.5*h*m2)
+  m4 <- f(x[i-1] + h, y[i-1] + h*m3)
+  x[i] <- x[i-1] + h
+  y[i] <- y[i-1] + h * (m1 + m4 + 2*m2 + 2*m3) / 6
+  
+  
+}
+
+g <- c()
+
+for (i in 1:3) {
+  g[i] <- f(x[i+1],y[i+1])
+  print(g[i])
+  
+}
+
+#Milne's formula
+Y1 <- y[1] + 4*h * (2*g[1] - g[2] + 2*g[3]) /3 
+cat("Solution obtained using Milne's method is", Y1,3)
+
+g[4] <- f(x[5],Y1)
+print(g[4])
+
+#Simpson formula
+Y2 <- y[3] + h * ( g[2] + 4*g[3] + g[4]) /3
+cat("Solution obtained using Simpson's method is", Y2,3)
+
+#Values are not approximated here ao value slightly differs from the textbook value
+\ No newline at end of file