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/EX16.1/16_1.pdf | Bin 0 -> 7048 bytes
 1332/CH16/EX16.1/16_1.sce |  33 ++++++++++++++++++++
 1332/CH16/EX16.2/16_2.pdf | Bin 0 -> 6238 bytes
 1332/CH16/EX16.2/16_2.sce |  75 ++++++++++++++++++++++++++++++++++++++++++++++
 1332/CH16/EX16.3/16_3.pdf | Bin 0 -> 6345 bytes
 1332/CH16/EX16.3/16_3.sce |  36 ++++++++++++++++++++++
 1332/CH16/EX16.4/16_4.pdf | Bin 0 -> 6480 bytes
 1332/CH16/EX16.4/16_4.sce |  52 ++++++++++++++++++++++++++++++++
 1332/CH16/EX16.5/16_5.pdf | Bin 0 -> 6403 bytes
 1332/CH16/EX16.5/16_5.sce |  29 ++++++++++++++++++
 1332/CH16/EX16.6/16_6.pdf | Bin 0 -> 6391 bytes
 1332/CH16/EX16.6/16_6.sce |  33 ++++++++++++++++++++
 12 files changed, 258 insertions(+)
 create mode 100755 1332/CH16/EX16.1/16_1.pdf
 create mode 100755 1332/CH16/EX16.1/16_1.sce
 create mode 100755 1332/CH16/EX16.2/16_2.pdf
 create mode 100755 1332/CH16/EX16.2/16_2.sce
 create mode 100755 1332/CH16/EX16.3/16_3.pdf
 create mode 100755 1332/CH16/EX16.3/16_3.sce
 create mode 100755 1332/CH16/EX16.4/16_4.pdf
 create mode 100755 1332/CH16/EX16.4/16_4.sce
 create mode 100755 1332/CH16/EX16.5/16_5.pdf
 create mode 100755 1332/CH16/EX16.5/16_5.sce
 create mode 100755 1332/CH16/EX16.6/16_6.pdf
 create mode 100755 1332/CH16/EX16.6/16_6.sce

(limited to '1332/CH16')

diff --git a/1332/CH16/EX16.1/16_1.pdf b/1332/CH16/EX16.1/16_1.pdf
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diff --git a/1332/CH16/EX16.1/16_1.sce b/1332/CH16/EX16.1/16_1.sce
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+//Example 16.1
+//Outline of Linear Shooting Method
+//Page no. 572
+clc;close;clear;
+
+deff('y=f(x)','y=x^2');
+h=0.5;X0=0;Y0=1;Z1=[-1,-1.5,-1.1771];i=1;Y1=Y0;
+for j=1:3
+    Z0=Z1(i);
+    i=i+1
+    Y0=1;
+    for n=1:2
+        printf('\nFor n = %i\n---------------------------\n',n-1)
+        K1(1)=h*Z0;
+        printf('\n K11 = %g',K1(1));
+        K1(2)=h*f(Y0);
+        printf('\n K12 = %g',K1(2));
+        K2=h*f(Y0+K1(2))
+        printf('\n K22 = %g',K2);
+        Z0=Z0+(K1(2)+K2)/2
+        printf('\n Z%i = %g',n,Z0);
+        K2=h*Z0;
+        printf('\n K21 = %g',K2);
+        Y0=Y0+(K1(1)+K2)/2
+        printf('\n Y%i = %g',n,Y0);
+        printf('\n\n\n')
+        if n==1 then
+            Y2=Y0
+        end
+    end
+    printf('\n\n\n')
+end
+printf('Hence the solution is y(%g) = %i, y(%g) = %.4f   and  y(%g) = %.1f',X0,Y1,X0+h,Y2,X0+2*h,Y0)
\ No newline at end of file
diff --git a/1332/CH16/EX16.2/16_2.pdf b/1332/CH16/EX16.2/16_2.pdf
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diff --git a/1332/CH16/EX16.2/16_2.sce b/1332/CH16/EX16.2/16_2.sce
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index 000000000..4bf89280f
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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
diff --git a/1332/CH16/EX16.3/16_3.pdf b/1332/CH16/EX16.3/16_3.pdf
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diff --git a/1332/CH16/EX16.3/16_3.sce b/1332/CH16/EX16.3/16_3.sce
new file mode 100755
index 000000000..2d907fcd4
--- /dev/null
+++ b/1332/CH16/EX16.3/16_3.sce
@@ -0,0 +1,36 @@
+//Example 16.3
+//Multiple Shooting Method
+//Page no. 577
+clc;close;clear;
+
+h=0.25;x=0;y1=0;
+deff('y=f(x)','y=-(4*h^2)/(1+x)^2')
+deff('y=f1(x)','y=-2*(1+(h^2)/(1+x)^2)')
+
+for i=1:4
+    x=x+h
+    B(i)=f(x);
+    for j=1:4
+        if i==4 & i==j
+            A(i,j)=f1(x)+1/4
+            A(i,j-1)=2
+        elseif j==i then
+            A(i,j)=f1(x)
+            A(i,j+1)=1
+            if j-1~=0 then
+                A(i,j-1)=1
+            end
+        end
+    end
+end
+y=inv(A)*B
+disp(B,"B =",A,'A = ')
+printf('\n\n\n x :')
+for i=1:5
+    printf('\t%.2f',x)
+    x=x+h
+end
+x=0;printf('\n y :\t%.2f',y1);
+for i=1:4
+    printf('\t%.4f',y(i))
+end
diff --git a/1332/CH16/EX16.4/16_4.pdf b/1332/CH16/EX16.4/16_4.pdf
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diff --git a/1332/CH16/EX16.4/16_4.sce b/1332/CH16/EX16.4/16_4.sce
new file mode 100755
index 000000000..d880ae40c
--- /dev/null
+++ b/1332/CH16/EX16.4/16_4.sce
@@ -0,0 +1,52 @@
+//Example 16.4
+//Finite Difference Method
+//Page no. 582
+clc;close;clear;
+
+x=0;h=0.25;q=-1;Y(1)=-2;Y(5)=1;
+printf('\n i\txi\tYi\tpi\tqi\tri\n-----------------------------------------------\n')
+for i=1:5
+    r(i)=-x^2
+    if i>1 & i<5 then
+        printf(' %i\t%g\t%s\t%g\t%i\t%g\n',i-1,x,"?",x,q,r(i))
+    else
+        printf(' %i\t%g\t%g\t%g\t%i\t%g\n',i-1,x,Y(i),x,q,r(i))
+    end
+    x=x+h
+end
+x=0;
+printf('-----------------------------------------------\n')
+for i=1:3
+    x=x+h
+    for j=1:3
+        if i==j then
+            A(i,j)=2+h^2*q
+        elseif i<j & abs(i-j)~=2
+            A(i,j)=-1+h*x/2
+        elseif i>j & abs(i-j)~=2
+            A(i,j)=-1-h*x/2
+        end
+    end
+    if i==3 then
+        B(i)=-h^2*r(i+1)+(-h*x/2+1)*Y(1+2*(i-1))
+    else
+        B(i)=-h^2*r(i+1)+(h*x/2+1)*Y(1+2*(i-1))
+    end
+    B(i)=(-1)^(i+1)*B(i)
+end
+disp(B,"B =",A,'A = ')
+y=inv(A)*B
+for i=1:3
+    Y(i+1)=y(i)
+end
+x=0;
+disp("The Solution is :",B,"B =",A,'A = ')
+printf(' x :')
+for i=1:5
+    printf('\t %.2f',x)
+    x=x+h
+end
+x=0;printf('\n y :');
+for i=1:5
+    printf('\t%.3f',Y(i))
+end
\ No newline at end of file
diff --git a/1332/CH16/EX16.5/16_5.pdf b/1332/CH16/EX16.5/16_5.pdf
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index 000000000..eca8efd81
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diff --git a/1332/CH16/EX16.5/16_5.sce b/1332/CH16/EX16.5/16_5.sce
new file mode 100755
index 000000000..c3604344a
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+++ b/1332/CH16/EX16.5/16_5.sce
@@ -0,0 +1,29 @@
+//Example 16.5
+//Non Linear Problem
+//Page no. 584
+clc;close;clear;
+
+deff('y=f(x)','y=2/(1+x)')
+Y=[1,0.75,0.75,0.75,0.5];h=0.25
+A=[-2,1,0;1,-2,1;0,1,-2];A_1=inv(A)
+disp(A_1,"Inverse of A =",A,"A =")
+printf('\nThe Solution of the system is: \n\n Iteration\t  Y0\t\t  Y1\t\t  Y2\t\t  Y3\t\t  Y4\n----------------------------------------------------------------------------------------')
+for i=0:6
+    printf('\n     %i',i)
+    for j=1:5
+        if j<4 & i~=0 then
+            Y(j+1)=y(j)
+        end
+        printf('\t\t%.4f',Y(j))
+    end
+    x=0;
+    for j=1:3
+        x=x+h
+        if j~=2 then
+            B(j)=h^2*f(x)*Y(j+1)^2-Y(1+2*(j-1))
+        else
+            B(j)=h^2*f(x)*Y(j+1)^2
+        end
+    end
+    y=A_1*B
+end
\ No newline at end of file
diff --git a/1332/CH16/EX16.6/16_6.pdf b/1332/CH16/EX16.6/16_6.pdf
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diff --git a/1332/CH16/EX16.6/16_6.sce b/1332/CH16/EX16.6/16_6.sce
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index 000000000..72049be59
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@@ -0,0 +1,33 @@
+//Example 16.6
+//Collocation Method
+//Page no. 589
+clc;close;clear;
+
+h1=0.000001;h=0.25;x=0;
+Y(1)=0;Y(5)=0;
+deff('y=p(x)','y=1')
+deff('y=q(x)','y=-2/(1+x)^2')
+deff('y=f(x)','y=(2*x-4)/(1+x)^4')
+deff('y=fi(x,j)','y=(1-x)*x^j')
+deff('y=f1(x,y)','y=(-x+y)/h1')   //function for differentiation
+for i=1:4
+    x=x+h
+    for j=1:4
+        A(i,j)=p(x)*f1(f1(fi(x,j),fi(x+h1,j)),f1(fi(x+h1,j),fi(x+2*h1,j)))+f1(p(x),p(x+h1))*f1(fi(x,j),fi(x+h1,j))+q(x)*fi(x,j)
+    end
+end
+x=0;
+for i=1:4
+    x=x+h
+    B(i)=f(x)
+end
+disp(B,'B =',A,"A =")
+C=inv(A)*B
+x=0;
+for i=2:4
+    x=x+h;
+    for j=1:4
+        Y(i)=Y(i)+C(j)*fi(x,j)
+    end
+end
+disp(Y,"Solution Matrix Y = ")
\ No newline at end of file
-- 
cgit