From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Tue, 10 Oct 2017 12:27:19 +0530
Subject: initial commit / add all books

---
 260/CH13/EX13.8/13_8.sce | 57 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 260/CH13/EX13.8/13_8.sce

(limited to '260/CH13/EX13.8')

diff --git a/260/CH13/EX13.8/13_8.sce b/260/CH13/EX13.8/13_8.sce
new file mode 100644
index 000000000..4d10fae11
--- /dev/null
+++ b/260/CH13/EX13.8/13_8.sce
@@ -0,0 +1,57 @@
+//Eg-13.8
+//pg-542
+
+clear
+clc
+close()
+x(1) = 0;
+x_ending = 200;
+l = 1000;    //no. of divisions
+h = (x_ending-x(1))/l;
+
+y5(1) = 0.01;
+y4(1) = 0.01;
+y(1) = 0.01;
+des = 10^(-5);
+deff('out = F(in1,in2)','out = in2^2*(1-in2)')
+//h = 0.5;
+for(i = 1:150)
+
+k1 = h*F(x(i),y(i));
+k2 = h*F(x(i) + 1/5*h,y(i)+1/5*k1);
+k3 = h*F(x(i) + 3/10*h,y(i)+3/40*k1 + 9/40*k2);
+k4 = h*F(x(i)+3/5*h,y(i) + 3/10*k1 - 9/10*k2 + 6/5*k3);
+k5 = h*F(x(i)+h, y(i - 11/54*k1 + 5/2*k2 - 70/27*k3 + 35/27*k4));
+k6 = h*F(x(i)+7/8*h, y(i) + 1631/55296*k1 + 175/512*k2 + 575/13824*k3 + 44275/110592*k4 + 253/4096*k5);
+
+y5(i+1) = y(i) + (37/378*k1 + 250/621*k3 + 125/594*k4 + 512/1771*k6);
+
+y4(i+1) = y(i) + (2825/27648*k1 + 18575/48384*k3 + 13525/55296*k4 + 277/14336*k5 + 1/4*k6);
+
+err = abs(y5(i+1) - y4(i+1));
+
+if(err > des)
+    n = 0.25;
+elseif(err < des)
+    n = 0.2;
+end
+
+h = h*(abs(des/err))^n;
+
+y(i+1) = y(i) + (37/378*k1 + 250/621*k3 + 125/594*k4 + 512/1771*k6);
+
+x(i+1) = x(i)+h;
+
+end 
+
+printf('The values calculated using RK Fehlberg method are tabulated below\n')
+printf('    x          y\n')
+for(i = 1:150)
+    printf('%f    %f\n',x(i),y(i))
+end
+
+plot(x,y)
+xlabel('t')
+ylabel('y')
+
+//There can be a difference in values this code gives and the code in the textbook gives because the author didn't mention the initial value of h that was used.Final value of x has been taken as 200 and 1000 divisions among will give h = (200-0)/1000.
\ No newline at end of file
-- 
cgit