e:\Bisection.txt
************************************************************************
clc;
clear all;
a=input('Initial point ');
b=input('Final Point ');
c=(a+b)/2;
f=@(x) x^3+4*(x^2)-10;
E=0.001;
ceil(n=(log(b-a)-log(E))/log(2))
while(abs(a-b)>E)
if f(a)*f(c)<0
b=c;
else
a=c;
end;
c=(a+b)/2;
end;
c
e:\Fixed_Point_Iteration.txt
************************************************************************
clc;
clear all;
a=input("a");
b=input('b');
%x0=(a+b)/2;
x0=1;
E=0.001;
N=ceil((log(b-a)-log(E))/(log(2)));
i=1;
g=@(x) x-((2*sin(3.14*x)+x)/(1+(2*3.14*cos(3.14*x)))); %Newton Method to find g(x);
while i<=N
xx=g(x0);
if(abs(xx-x0)<E)
break;
end;
x0=xx;i=i+1;
end;
xx
e:\Guass_Elimination.txt
************************************************************************
clc;
clear all;
n=input('N: ');
for i=1:n
for j=1:n+1
A(i,j)=input('Enter element');
end;
end;
for i=1:n-1
for j=i+1:n
m=A(j,i)/A(i,i);
for k=1:n+1
A(j,k)=A(j,k)-m*A(i,k);
end;
end;
end;
X(n)=A(n,n+1)/A(n,n);
for i=(n-1):-1:1
sum=0;
for j=i+1:n
sum=sum+(A(i,j)*X(j));
end;
X(i)=(A(i,n+1)-sum)/A(i,i);
end;
A
X
e:\GuassSeidal.txt
************************************************************************
clc;
clear all;
n=input('N ');
E=0.0001;
for i=1:n
for j=1:n+1
A(i,j)=input('Enter element');
end;
end;
for i=1:n
X(i)=0;
Xold(i)=0;
end;
sum=0;
normval=2;
while abs(normval)>E
Xold=X;
for i=1:n
for j=1:n
if j!=i
sum=sum+A(i,j)*X(j);
end;
end;
X(i)=(A(i,n+1)-sum)/A(i,i);
sum=0;
end;
normval=norm(Xold-X,inf);
end;
X
e:\Lagrange_Interpolation.txt
************************************************************************
% Q3
clc;
clear all;
n=input('N: ');
f=@(x) exp(2*x)*cos(3*x);
for i=1:n
X(i)=input('Enter X: ');
%Y(i)=input('Enter Y: ');
Y(i)=f(X(i));
l(i)=1;
end;
p=input('Enter the value of X where value is to be calculated');
for i=1:n
for j=1:n
if i!=j
l(i)=((p-X(j))/(X(i)-X(j)))*l(i);
end;
end;
end;
sum=0;
for i=1:n
sum=sum+l(i)*Y(i);
end;
sum
e:\Newton.txt
************************************************************************
clc;
clear all;
a=input('a ');
E=0.0001;
f=@(x) cos(x)-(x*exp(x));
g=@(x) -sin(x)-(x*exp(x)+exp(x));
while(true)
b=a-(f(a)/g(a));
if(abs(b-a)<=E)
break;
end;
a=b;
end;
b
e:\Newton_Divided_Difference_Interpolation.txt
************************************************************************
clc;
clear all;
n=input('N ');
p=input('p ');
for i=1:n
X(i)=input('X');
Y(i)=input('Y');
end;
for i=1:n
F(1,i)=Y(i);
end;
for i=2:n
for j=i:n
F(i,j)=(F(i-1,j)-F(i-1,j-1))/(X(j)-X(j-i+1));
end;
end;
for i=1:n
product(i)=1;
for j=1:(i-1)
product(i)=product(i)*(p-X(j));
end;
end;
F=transpose(F);
sum=0;
for i=1:n
sum=sum+F(i,i)*product(i);
end;
sum
e:\Power_Method.txt
************************************************************************
clc;
clear all;
n=input('N: ');
E=0.001;
for i=1:n
for j=1:n
A(i,j)=input('Enter Element');
end;
end;
for i=1:n
X(i)=input('Element');
end;
X=transpose(X);
Y=A*X;
K=norm(Y,inf);
Kdash=100;
X=(1/K)*Y;
while abs(K-Kdash) >E
Y=A*X;
Kdash=K;
K=norm(Y,inf);
X=(1/K)*Y;
end;
K
X
e:\RungeKutta.txt
************************************************************************
clc;
clear all;
a=input('a ');
b=input('b ');
h=input('h ');
n=(b-a)/h;
f=@(t,y) -y+(2*cos(t));
t0=0;y0=1;
for i=1:n
k1=h*f(t0,y0);
k2=h*f((t0+(h/2)),(y0+(k1/2)));
k3=h*(f((t0+(h/2)),(y0+(k2/2))));
k4=h*(f(t0+h,y0+k3));
y1=y0+(1/6)*(k1+2*k2+2*k3+k4);
y0=y1;
t0=t0+h;
end;
y1
e:\Secant.txt
************************************************************************
clc;
clear all;
a=input('a ');
b=input('b ');
c=0;
E=0.0001;
f=@(x) x^2-17;
while(abs(b-a)>E)
c=b-((b-a)/(f(b)-f(a)))*f(b);
if(f(c)==0)
break;
end;
a=b;
b=c;
end;
b
e:\Simpson.txt
************************************************************************
clc;
clear all;
a=input('a ');
b=input('b ');
N=input('N ');
h=(b-a)/N;
f=@(x) 1/(x*log(x));
sum=0;
for i=1:N-1
x=a+(i*h);
if i%2==0
sum=sum+(2*f(x));
else
sum=sum+(4*f(x));
end;
sum=(sum+f(a)+f(b));
end;
sum*(h/3)
e:\Trepozoidal.txt
************************************************************************
clc;
clear all;
a=input('a ');
b=input('b ');
N=input('N ');
h=(b-a)/N;
f=@(x) cos(x)*cos(x);
sum=0;
I=0;
for i=1:N-1
x=a+(i*h);
sum=sum+(2*f(x));
% Sum starts as Sigma i=1 to N-1 because f(a) and f(b) are adjusted later
end;
sum=sum+(f(a)+f(b));
sum*(h/2)
% I= h/2 * ( f(a) +f(b) ) + h*( sigma i=1 to N-1 f(a+h*i) )
