From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 1332/CH16/EX16.2/16_2.pdf | Bin 0 -> 6238 bytes
 1332/CH16/EX16.2/16_2.sce |  75 ++++++++++++++++++++++++++++++++++++++++++++++
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 create mode 100755 1332/CH16/EX16.2/16_2.pdf
 create mode 100755 1332/CH16/EX16.2/16_2.sce

(limited to '1332/CH16/EX16.2')

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+//Example 16.2
+//Linear Shooting Method
+//Page no. 576
+clc;close;clear;
+
+deff('y=f1(x,y,y1)','y=-x*y1+x^2*y+2*x^3')
+deff('y=F1(x,y,y1)','y=-x*y1+x^2*y+2*x^3')
+deff('y=F2(x,y,y1)','y=-x*y1+x^2*y')
+a=0;b=1;
+y0=1;y1=-1;n=5;
+h=(b-a)/n
+y=y0;y01=0;x=a;
+for i=0:5
+    yi1(1,i+1)=y
+    K1=h*y01;
+    R1=h*F1(x,y,y01);
+    K2=h*(y+R1/2);
+    R2=h*F1(x+h/2,y+K1/2,y01+R1/2)
+    K3=h*(y01+R2/2)
+    R3=h*F1(x+h/2,y+K2/2,y01+R2/2)
+    K4=h*(y+R3)
+    R4=h*F1(x+h,y+K3,y01+R3)
+    y=y+(K1+2*K2+2*K3+K4)/6
+    y01=y01+(R1+2*R2+2*R3+R4)/6
+    x=x+h
+end
+y=0;y01=1;x=a;
+for i=0:5
+    yi2(1,i+1)=y
+    K1=h*y01;
+    R1=h*F2(x,y,y01);
+    K2=h*(y+R1/2);
+    R2=h*F2(x+h/2,y+K1/2,y01+R1/2)
+    K3=h*(y01+R2/2)
+    R3=h*F2(x+h/2,y+K2/2,y01+R2/2)
+    K4=h*(y+R3)
+    R4=h*F2(x+h,y+K3,y01+R3)
+    y=y+(K1+2*K2+2*K3+K4)/6
+    y01=y01+(R1+2*R2+2*R3+R4)/6
+    x=x+h
+end
+for i=1:6
+    yi(i)=yi1(1,i)+((y1-yi1(6))/yi2(6))*yi2(i)
+end
+y=1;x=a;y01=y1
+for i=0:5
+    yir(1,i+1)=y;
+    K1=h*y01;
+    R1=h*f1(x,y,y01);
+    K2=h*(y+R1/2);
+    R2=h*f1(x+h/2,y+K1/2,y01+R1/2)
+    K3=h*(y01+R2/2)
+    R3=h*f1(x+h/2,y+K2/2,y01+R2/2)
+    K4=h*(y+R3)
+    R4=h*f1(x+h,y+K3,y01+R3)
+    y=y+(K1+2*K2+2*K3+K4)/6
+    y01=y01+(R1+2*R2+2*R3+R4)/6
+    x=x+h
+end
+x=a;
+printf('\n   ------------------------------------------------------------------------------------------------------\n\tx')
+for i=1:6
+    printf('\t%.1f\t',x)
+    x=x+h
+end
+printf('\n\ty')
+for i=1:6
+    printf('\t%.4f\t',yi(i))
+end
+printf('\n    by RK')
+for i=1:6
+    printf('\t%.4f\t',yir(i))
+end
+printf('\n   ------------------------------------------------------------------------------------------------------')
+printf('\n\n\nNote: Computation error in calculation of values by RK method performed in book')
\ No newline at end of file
-- 
cgit