tp

1) Curve Fitting

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A.Straight Line

n = input ('enter the number of inputs   :');

x = zeros(n);y = zeros(n);

for i= 1:n

   fprintf('Enter the value of x %d ',i);

   x(i) = input (':');

end

for i =1:n

   fprintf('Enter the value of y %d ',i);

   y(i) = input (':');

end

s0 = 0;

s1 = 0;

s2 = 0;

s3 = 0;

fprintf ('x           y           x*x           x*y ');

for i = 1:n

   s0 = s0 + x(i);

   s1 = s1 + y(i);

   s2 = s2 + x(i)*x(i);

   s3 = s3 + x(i)*y(i);

   fprintf( '\n %f %f \t %f \t \t%f\n', x(i),y(i), x(i)*x(i) , x(i)*y(i) ); 

end

fprintf('____________________________________________________');

fprintf( '\n %f %f \t %f \t \t%f\n', s0,s1, s2 , s3 );   

%two equation's are

%a*s0 + n*b = s1

%a*s2 + b*s0 = s3

m = [s0 n; s2 s0];

n = [s1;s3];

p = linsolve(m,n)

fprintf ('\n best line fit is   " (%f) x  + (%f)    " ',p(1),p(2));

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B.Power Eqn

n=input('Enter number of data points : ');

for i=1:n

   x(i)=input('Enter value of x : ');

   y=input('Enter corresponding value of y : ');

  Y(i)= log(y);

end

S0=0;

S1=0;

S2=0;

S3=0;

for i=1:n

   S0=S0+x(i);

   S1=S1+Y(i);

   S2=S2+x(i)*Y(i);

   S3=S3+x(i)*x(i);

end

d=S0*S0-n*S3;

da=S1*S0-n*S2;

db=S0*S2-S1*S3;

a1=da/d;

b1=db/d;

a=exp(b1);

b=exp(a1);

fprintf('Ans a=%f  b=%f',a,b)

fprintf('y = %fx + %f ',a,b);

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C.Least Square Power Equation

n=input('Enter number of data points :');

for i=1:n

x(i)=input('Enter value of x:');

y(i)=input('Enter corresponding value of y:');

end

In_x=0;

In_y=0;

In_xy=0;

In_x2=0;

for i=1:n

   In_x=In_x+reallog(x(i));

   In_y=In_y+reallog(y(i));

   In_xy=In_xy+reallog(x(i))*reallog(y(i));

   In_x2=In_x2+power(reallog(x(i)),2);

end

b=(n*In_xy-In_x*In_y)/(n*In_x2-power(In_x,2));

r=(In_y/n)-(b*In_x/n);

a=exp(r);

fprintf('y=%f(%f^x)',a,b);

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D.Exponential Eqn

n=input('Enter number of data points : ');

for i=1:n

   x(i)=input('Enter value of x : ');

   y=input('Enter corresponding value of y : ');

  Y(i)= log(y);

end

S0=0;

S1=0;

S2=0;

S3=0;

for i=1:n

   S0=S0+x(i);

   S1=S1+Y(i);

   S2=S2+x(i)*Y(i);

   S3=S3+x(i)*x(i);

end

d=S0*S0-n*S3;

da=S1*S0-n*S2;

db=S0*S2-S1*S3;

a1=da/d;

b1=db/d;

a=exp(b1);

b=a1;

fprintf('Ans a=%f  b=%f',a,b)

fprintf('y = (%f)e^(%f)x',a,b);

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2) ODE

A.Euler's

f=inline('(-x*y*y)');

x0 = input('\nEnter the value of x0  :');

y0 = input('Enter the value of y0  :');

xg = input('Enter the value of xg  :');

h = input ('Enter the stepsize     :');

n = (xg-x0)/h;

for i= 1:n

yg = y0 + h*f(x0,y0);

x0 = x0+h;

   y0 = yg;

fprintf('\n f(x(%d ,%d) is %f ',i,i,h*f(x0,y0));

end

fprintf('\n The final value of yg = %f',yg);

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B.RK 4th order

f=inline('(x*x+y*y)');

x0 = input('\nEnter the value of x0  :');

y0 = input('Enter the value of y0  :');

xg = input('Enter the value of xg  :');

h = input ('Enter the stepsize     :');

n = (xg-x0)/h;

for i= 1:n

   k1 = h*f(x0,y0);

   k2 = h*f((x0+(h/2),(y0+(k1/2));

   k3 = h*f((x0+(h/2),(y0+(k2/2));

   k4 = h*f((x0+h),(y0+k3));

   k = (k1+2*k2+2*k3+k4)/6;

yg = y0 + k;

x0 = x0+h;

   y0 = yg;

end

fprintf('\n The final value of yg = %f',yg);

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C.RK 2nd

f=inline('(x+y*z)');

 g=inline('(x*x-y*y+0*z)');

 x0=input('Enter value of x0 ');

 y0=input('Enter value of y0 ');

 z0=input('Enter value of z0 '); 

 xg=input('Enter value of xg ');

h=input('Enter value of step size h= ');

n=(xg-x0)/h;

for i=1:n

   k1=h*f(x0,y0,z0);

   l1=h*g(x0,y0,z0);

   k2=h*f(x0+h,y0+k1*h,z0+l1);

   l2=h*g(x0+h,y0+k1,z0+l1);

   k=(k1+k2)/2;

   l=(l1+l2)/2;

   y0=y0+k;

   x0=x0+h;

   z0=z0+l;

end

fprintf('yg=%f and zg=%f',y0,z0);

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