ExampleTrapzodial Law

clc
clear

% %Trapezodial Rule

x0=7;
Length=7;
number_of_points=70;
dx=Length/number_of_points;
number_of_sections=number_of_points-1;

%Generating the number of points

N=number_of_points;

%For a case starting from the center of coordanites, this is the absoulute
%value for the node number

xx(1)=0;

%This is just a counter relating to where the process starts

for i=1:N-1
xx(i+1)=xx(i)+1;
end

%This calculates the coordanites of the studied nodes in the x direction

for i=1:N;
x(i)=xx(i)*dx+x0;
end

%This calculates the coordanites of the studied nodes in the y direction
%acoording to the studied function

for i=1:N;
y(i)=1/(1+x(i)^2);
end

for i=1:N;
    if (i==1) | (i==N)
        a(i)=y(i);
    elseif (i>1)
        b(i)=y(i);
    end
end

b(N)=0;
aa=sum(a(:));
bb=sum(b(:));
Area=0.5*dx*(aa+2*bb);
plot(x,y)
grid on
title('The Studied Area')
figure(1)

Newton Raphson

clc
clear

x1=4;
x2=5;
N=50000;
dx=(x2-x1)/N;
j=-1;
for i=1:N;
    j=j+1;
    x(i)=j*dx+x1;
end

for i=1:N;
 y(i)=(x(i))^2-5*x(i)+2;
 yp(i)=2*x(i)-5;
 a(i)=y(i)/yp(i);
end
xx=0;
for i=1:N
 xx=xx+x(i)-a(i);
end
x'
%plot(x)
plot(y)

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