initial commit / add all books

12 files changed, 258 insertions, 0 deletions

diff --git a/1332/CH16/EX16.1/16_1.pdf b/1332/CH16/EX16.1/16_1.pdf
new file mode 100755
index 000000000..22caad1e1
--- /dev/null
+++ b/1332/CH16/EX16.1/16_1.pdf
diff --git a/1332/CH16/EX16.1/16_1.sce b/1332/CH16/EX16.1/16_1.sce
new file mode 100755
index 000000000..a4883eb81
--- /dev/null
+++ b/1332/CH16/EX16.1/16_1.sce
@@ -0,0 +1,33 @@
+//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
new file mode 100755
index 000000000..07065af81
--- /dev/null
+++ b/1332/CH16/EX16.2/16_2.pdf
diff --git a/1332/CH16/EX16.2/16_2.sce b/1332/CH16/EX16.2/16_2.sce
new file mode 100755
index 000000000..4bf89280f
--- /dev/null
+++ b/1332/CH16/EX16.2/16_2.sce
@@ -0,0 +1,75 @@
+//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
new file mode 100755
index 000000000..5bb88e031
--- /dev/null
+++ b/1332/CH16/EX16.3/16_3.pdf
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
new file mode 100755
index 000000000..1cfe37ab0
--- /dev/null
+++ b/1332/CH16/EX16.4/16_4.pdf
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
new file mode 100755
index 000000000..eca8efd81
--- /dev/null
+++ b/1332/CH16/EX16.5/16_5.pdf
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
--- /dev/null
+++ 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
new file mode 100755
index 000000000..cee0b88fa
--- /dev/null
+++ b/1332/CH16/EX16.6/16_6.pdf
diff --git a/1332/CH16/EX16.6/16_6.sce b/1332/CH16/EX16.6/16_6.sce
new file mode 100755
index 000000000..72049be59
--- /dev/null
+++ b/1332/CH16/EX16.6/16_6.sce
@@ -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