From b3f3a8ecd454359a2e992161844f2fb599f8238a Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Fri, 4 Oct 2019 12:24:07 +0530
Subject: Initial commit/added all books

---
 .../CH11/EX11.8/Ex11_8.R                           | 40 ++++++++++++++++++++++
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 create mode 100644 Numerical_Methods_by_E_Balaguruswamy/CH11/EX11.8/Ex11_8.R

(limited to 'Numerical_Methods_by_E_Balaguruswamy/CH11/EX11.8')

diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH11/EX11.8/Ex11_8.R b/Numerical_Methods_by_E_Balaguruswamy/CH11/EX11.8/Ex11_8.R
new file mode 100644
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--- /dev/null
+++ b/Numerical_Methods_by_E_Balaguruswamy/CH11/EX11.8/Ex11_8.R
@@ -0,0 +1,40 @@
+# Example 8     Chapter 11       Page no.: 364
+# Richardson Extrapolation
+
+f <- function(x){
+  return(exp(x))
+}
+h1<- 0.5
+r1 <- 1/2
+x1<- 0.5
+
+#First order forward difference formula
+D1 <- function(x,h) {
+  return((f(x+h) - f(x-h))/(2*h))
+}
+
+Dr1 <- function(x,r,h){
+  return((f(x+(r*h)) - f(x-(r*h)))/(2*r*h))
+} 
+
+f1 <- function(x,r,h){
+  return((Dr1(x,r,h)-(r^2)*D1(x,h))/(1-(r^2)))
+}
+F <- signif(f1(x1,r1,h1), digits = 5)
+
+cat("The value of function e^x at",x1," with parameters")
+cat("h=",h1)
+cat("r=",r1)
+cat("is",F)
+
+# The value deviates slighly from the value of the textbook becaues of approximation in the text
+
+r2 <- 2
+F1 <- signif(f1(x1,r2,h1), digits = 5)
+
+cat("The value of function e^x at",x1," with parameters")
+cat("h=",h1)
+cat("r=",r2)
+cat("is",F1)
+
+cat(" This shows that estimate with r=",r1,"is better than the estimate with r=",2)
\ No newline at end of file
-- 
cgit