5 files changed, 187 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
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--- /dev/null
+++ b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.10/Ex13_10.R
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+# 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
diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.4/Ex13_4.R b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.4/Ex13_4.R
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--- /dev/null
+++ b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.4/Ex13_4.R
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+# Example 4     Chapter 13       Page no.: 420
+# Euler Method
+
+#for the first solution
+cat("Case A:")
+h <- 0.5
+x <- 1
+y <- 2
+cat("h=",h)
+#Creating algorithm and displaying
+for (i in 1:2) {
+  
+  dy <- (3 * (x *x)) + 1
+  y <- y + (h * dy)
+  x <- x +  h
+  cat("y(",x,")= ",y,"\n")
+}
+
+#for the second solution
+cat("Case B:")
+h <- 0.25
+x <- 1
+y <- 2
+cat("h=",h)
+
+print(x)
+print(y)
+
+#Creating algorithm and displaying
+for (i in 1:5) {
+  
+  cat("y(",x,")= ",y,"\n")
+  x <- x +  h
+  dy <- (3 * ((x-h)^2)) + 1
+  y <- y + (h * dy)
+  
+  
+}
+
+#For Case B, textbook answer is false.
+\ No newline at end of file
diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.6/Ex13_6.R b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.6/Ex13_6.R
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--- /dev/null
+++ b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.6/Ex13_6.R
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+# Example 6     Chapter 13       Page no.: 427
+# Heun Method and Euler Method
+
+#for the solution - Euler method
+cat("Case A: Euler's Method")
+h <- 0.25
+x <- 1
+y <- 2
+cat("h=",h)
+cat("x=",x)
+cat("y=",y)
+
+#Creating euler algorithm and displaying
+for (i in 1:5) {
+  
+  cat("y(",x,")= ",y,"\n")
+  x <- x +  h
+  f <- (2 * y / (x-h))
+  y <- y + (h * f)
+
+}
+
+#for the solution - Heun's method
+cat("Case B: Heun's Method")
+h <- 0.25
+x <- 1
+y <- 2
+cat("h=",h)
+
+#Creating heun algorithm and displaying
+for (i in 1:4) {
+  
+  
+  f1 <- (2 * y / (x))
+  m <- y + h*f1
+  f2 <- (2 * m / (x+h))
+  y <- y + ((h/2) * (f1 + f2))
+  x <- x +  h
+  cat("y(",x,")= ",y,"\n")
+  
+}
+
+#Values slightly differ but are more precise than what is given in the textbook 
+\ No newline at end of file
diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.7/Ex13_7.R b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.7/Ex13_7.R
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+++ b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.7/Ex13_7.R
@@ -0,0 +1,21 @@
+# Example 7     Chapter 13       Page no.: 433
+# Polygon Method
+
+#for the solution
+cat("Polygon Method")
+h <- 0.25
+x = 1
+y = 2
+cat("h=",h)
+cat("x=",x)
+cat("y=",y)
+
+#Creating algorithm and displaying
+for (i in 1:3) {
+  
+  cat("y(",x,")= ",signif(y,3),"\n")
+  f1 <- (2 * y / x)
+  f2 <- (2 * (y + ( h * f1 / 2 ) ) / (x + ( h / 2 ) ))
+  x <- x +  h
+  y <- y + (h * f2)
+}
diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.8/Ex13_8.R b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.8/Ex13_8.R
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--- /dev/null
+++ b/Numerical_Methods_by_E_Balaguruswamy/CH13/EX13.8/Ex13_8.R
@@ -0,0 +1,30 @@
+# Example 8     Chapter 13       Page no.: 439
+# Classic Runge Kutta Method
+
+#for the solution
+cat("Classic Runge Kutta Method")
+h <- 0.2
+x = 0
+y = 0
+
+cat("h=",h)
+cat("x=",x)
+cat("y=",y)
+
+#Given Function
+f <- function(x,y){
+  x^2 + y^2
+}
+
+#Creating algorithm and displaying
+for (i in 1:2) {
+  
+  m1 <- f(x,y)
+  m2 <- f(x + 0.5*h, y + 0.5*h*m1)
+  m3 <- f(x + 0.5*h, y + 0.5*h*m2)
+  m4 <- f(x + h, y + h*m3)
+  x <- x + h
+  y <- y + h * (m1 + m4 + 2*m2 + 2*m3) / 6
+  cat("y(",x,")= ", signif(y,6),"\n")
+  
+}