initial commit / add all books

11 files changed, 257 insertions, 0 deletions

diff --git a/60/DEPENDENCIES/adamsbash.sce b/60/DEPENDENCIES/adamsbash.sce
new file mode 100755
index 000000000..41210017d
--- /dev/null
+++ b/60/DEPENDENCIES/adamsbash.sce
@@ -0,0 +1,27 @@
+
+function [u,t] = adamsbashforth3(u0,t0,tn,h,f)
+
+//adamsbashforth3 3rd order method solving ODE
+//  du/dt = f(u,t), with initial 
+//conditions u=u0 at t=t0.  The 
+//solution is obtained for t = [t0:h:tn]
+//and returned in u
+
+umaxAllowed = 1e+100;
+
+t = [t0:h:tn]; u = zeros(t); n = length(u); u(1) = u0;
+for j = 1:n-1
+if j<3 then
+      k1=h*f(t(j),u(j));
+    k2=h*f(t(j)+h,u(j)+k1);
+	u(j+1) = u(j) + (k2+k1)/2;
+end;  
+   
+if j>=2 then
+       u(j+2) = u(j+1) + (h/12)*(23*f(t(j+1),u(j+1))-16*f(t(j),u(j))+5*f(t(j-1),u(j-1)));
+end;
+end;
+endfunction
+ 
+
+
diff --git a/60/DEPENDENCIES/bisect.sce b/60/DEPENDENCIES/bisect.sce
new file mode 100755
index 000000000..23216d2bf
--- /dev/null
+++ b/60/DEPENDENCIES/bisect.sce
@@ -0,0 +1,28 @@
+function x=bisection(a,b,f)
+    N=100;                                      //define max. number of iterations
+    PE=10^-4                                  //define tolerance
+    if (f(a)*f(b) > 0) then
+	     error('no root possible f(a)*f(b) > 0')    // checking if the decided range is containing a root
+	      abort;
+    end;
+    if(abs(f(a)) <PE) then
+	    error('solution at a')                    // seeing if there is an approximate root at a,
+	     abort;
+    end;
+    if(abs(f(b)) < PE) then                       //seeing if there is an approximate root at b,
+	error('solution at b')
+	abort;
+    end;
+    x=(a+b)/2
+    for n=1:1:N                                   //initialising 'for' loop,
+        p=f(a)*f(x)
+        if p<0 then b=x ,x=(a+x)/2;                //checking for the required conditions( f(x)*f(a)<0),
+        else
+             a=x
+            x=(x+b)/2;
+        end
+        if abs(f(x))<=PE then break                // instruction to come out of the loop after the required condition is achived,   
+        end
+    end
+    disp(n," no. of iterations =")                 // display the no. of iterations took to achive required condition,
+endfunction
\ No newline at end of file
diff --git a/60/DEPENDENCIES/fixedp.sce b/60/DEPENDENCIES/fixedp.sce
new file mode 100755
index 000000000..f4031a234
--- /dev/null
+++ b/60/DEPENDENCIES/fixedp.sce
@@ -0,0 +1,23 @@
+function [x]=fixedp(x0,f)

+//fixed-point iteration

+N = 100; eps = 1.e-5; // define max. no. iterations and error

+maxval = 10000.0;     // define value for divergence

+a = x0;

+while (N>0)

+	xn = f(a);

+	if(abs(xn-a)<eps)then

+		x=xn

+		disp(100-N);

+		return(x);

+	end;

+	if (abs(f(x))>maxval)then

+		disp(100-N);

+		error('Solution diverges');

+		abort;

+	end;

+	N = N - 1;

+	xx = xn;

+end;

+error('No convergence');

+abort;

+//end function

diff --git a/60/DEPENDENCIES/gausselim2.sce b/60/DEPENDENCIES/gausselim2.sce
new file mode 100755
index 000000000..9e1ef25f3
--- /dev/null
+++ b/60/DEPENDENCIES/gausselim2.sce
@@ -0,0 +1,43 @@
+function [x] = gausselim(A,b)
+
+    //This function obtains the solution to the system of 
+    //linear equations A*x = b, given the matrix of coefficients A
+    //and the right-hand side vector, b
+
+[nA,mA] = size(A)
+[nb,mb] = size(b)
+
+if nA<>mA then
+	error('gausselim - Matrix A must be square');
+	abort;
+elseif mA<>nb then
+        error('gausselim - incompatible dimensions between A and b');
+	abort;
+end;
+
+a = [A b];
+
+    //Forward elimination
+
+n = nA; 
+for k=1:n-1
+    for i=k+1:n
+	for j=k+1:n+1
+		a(i,j)=a(i,j)-a(k,j)*a(i,k)/a(k,k);
+	end;
+    end; 
+end;
+
+    //Backward substitution
+
+x(n) = a(n,n+1)/a(n,n);
+
+for i = n-1:-1:1
+	sumk=0
+	for k=i+1:n
+		sumk=sumk+a(i,k)*x(k); 
+	end; 
+	x(i)=(a(i,n+1)-sumk)/a(i,i); 
+end;
+
+    //End function
\ No newline at end of file
diff --git a/60/DEPENDENCIES/modifiedEuler.sce b/60/DEPENDENCIES/modifiedEuler.sce
new file mode 100755
index 000000000..164e09842
--- /dev/null
+++ b/60/DEPENDENCIES/modifiedEuler.sce
@@ -0,0 +1,28 @@
+function [u,t] = modifiedeuler(u0,t0,tn,h,f)
+
+//modifiedeuler 1st order method solving ODE
+//  du/dt = f(u,t), with initial 
+//conditions u=u0 at t=t0.  The 
+//solution is obtained for t = [t0:h:tn]
+//and returned in u
+
+umaxAllowed = 1e+100;
+
+t = [t0:h:tn]; u = zeros(t); n = length(u); u(1) = u0;
+
+for j = 1:n-1
+    k1=h*f(t(j),u(j));
+    k2=h*f(t(j)+h/2,u(j)+k1/2);
+    u(j+1) = u(j) + k2;
+   if u(j+1) > umaxAllowed then
+           disp('Euler 1 - WARNING: underflow or overflow');
+           disp('Solution sought in the following range:');
+           disp([t0 h tn]);
+          disp('Solution evaluated in the following range:');
+          disp([t0 h t(j)]);
+           n = j; t = t(1,1:n); u = u(1,1:n);
+    break;
+    end;
+end;
+
+endfunction
\ No newline at end of file
diff --git a/60/DEPENDENCIES/newt.sce b/60/DEPENDENCIES/newt.sce
new file mode 100755
index 000000000..6f7557e38
--- /dev/null
+++ b/60/DEPENDENCIES/newt.sce
@@ -0,0 +1,16 @@
+function x=newton(x,f,fp)
+    R=100;
+    PE=10^-8;
+    maxval=10^4;
+        
+    for n=1:1:R
+        x=x-f(x)/fp(x); 
+        if abs(f(x))<=PE then break
+        end
+        if (abs(f(x))>maxval) then error('Solution diverges');
+            abort
+            break
+        end
+    end
+    disp(n," no. of iterations =")
+endfunction
\ No newline at end of file
diff --git a/60/DEPENDENCIES/regulfalsi.sce b/60/DEPENDENCIES/regulfalsi.sce
new file mode 100755
index 000000000..a743b4a4f
--- /dev/null
+++ b/60/DEPENDENCIES/regulfalsi.sce
@@ -0,0 +1,13 @@
+function [x]=regularfalsi(a,b,f)

+    N=100;

+    PE=10^-5;

+    for n=2:1:N

+        x=a-(a-b)*f(a)/(f(a)-f(b));

+        disp(x)

+        if abs(f(x))<=PE then break;

+        elseif (f(a)*f(x)<0) then b=x;

+            else a=x;

+        end

+    end

+    disp(n," no. of ittirations =")

+endfunction
\ No newline at end of file
diff --git a/60/DEPENDENCIES/rkm2.sce b/60/DEPENDENCIES/rkm2.sce
new file mode 100755
index 000000000..633ecf265
--- /dev/null
+++ b/60/DEPENDENCIES/rkm2.sce
@@ -0,0 +1,26 @@
+function [u,t] = RK2(u0,t0,tn,h,f)
+
+//  RK2 method solving ODE
+//  du/dt = f(u,t), with initial  
+//conditions u=u0 at t=t0.  The 
+//solution is obtained for t = [t0:h:tn]
+//and returned in u
+
+umaxAllowed = 1e+100;
+
+t = [t0:h:tn]; u = zeros(t); n = length(u); u(1) = u0;
+
+for j = 1:n-1
+    k1=h*f(t(j),u(j));
+    k2=h*f(t(j)+h,u(j)+k1);
+    u(j+1) = u(j) + (1/2)*(k1+k2);
+   if u(j+1) > umaxAllowed then
+           disp('Euler 1 - WARNING: underflow or overflow');
+      disp('Solution sought in the following range:');
+           disp([t0 h tn]);
+      disp('Solution evaluated in the following range:');
+      disp([t0 h t(j)]);
+           n = j; t = t(1,1:n); u = u(1,1:n);
+       break;
+ end;
+end;
\ No newline at end of file
diff --git a/60/DEPENDENCIES/rkm4.sce b/60/DEPENDENCIES/rkm4.sce
new file mode 100755
index 000000000..d034c374b
--- /dev/null
+++ b/60/DEPENDENCIES/rkm4.sce
@@ -0,0 +1,28 @@
+function [u,t] = RK4(u0,t0,tn,h,f)
+//  RK4 method solving ODE
+//  du/dt = f(u,t), with initial  
+//conditions u=u0 at t=t0.  The 
+//solution is obtained for t = [t0:h:tn]
+//and returned in u
+
+umaxAllowed = 1e+100;
+
+t = [t0:h:tn]; u = zeros(t); n = length(u); u(1) = u0;
+
+for j = 1:n-1
+    k1=h*f(t(j),u(j));
+    k2=h*f(t(j)+h/2,u(j)+k1/2);
+    k3=h*f(t(j)+h/2,u(j)+k2/2);
+    k4=h*f(t(j)+h,u(j)+k3);
+    u(j+1) = u(j) + (1/6)*(k1+2*k2+2*k3+k4);
+    if u(j+1) > umaxAllowed then
+           disp('Euler 1 - WARNING: underflow or overflow');
+      disp('Solution sought in the following range:');
+           disp([t0 h tn]);
+      disp('Solution evaluated in the following range:');
+      disp([t0 h t(j)]);
+           n = j; t = t(1,1:n); u = u(1,1:n);
+       break;
+    end;
+end;
+  
diff --git a/60/DEPENDENCIES/scant.sce b/60/DEPENDENCIES/scant.sce
new file mode 100755
index 000000000..e7d914803
--- /dev/null
+++ b/60/DEPENDENCIES/scant.sce
@@ -0,0 +1,12 @@
+function [x]=secant(a,b,f)
+    N=100;             // define max. no. iterations to be performed
+    PE=10^-4           // define tolerance for convergence
+     for n=1:1:N       // initiating for loop
+        x=a-(a-b)*f(a)/(f(a)-f(b));  
+        if abs(f(x))<=PE then break; //checking for the required condition
+        else a=b;
+            b=x;
+        end     
+     end
+     disp(n," no. of iterations =") //
+endfunction
\ No newline at end of file
diff --git a/60/DEPENDENCIES/secantm.sce b/60/DEPENDENCIES/secantm.sce
new file mode 100755
index 000000000..fa0f84e78
--- /dev/null
+++ b/60/DEPENDENCIES/secantm.sce
@@ -0,0 +1,13 @@
+function [x]=secant(a,b,f)
+    N=100;             // define max. no. iterations to be performed
+    PE=10^-4           // define tolerance for convergence
+     for n=1:1:N       // initiating for loop
+        x=a-(a-b)*f(a)/(f(a)-f(b));  
+        disp(x)
+        if abs(f(x))<=PE then break; //checking for the required condition
+        else a=b;
+            b=x;
+        end     
+     end
+     disp(n," no. of iterations =") //
+endfunction
\ No newline at end of file