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Gauss seidel

A=input("Enter the matrix A : ")
b=input("Enter the matrix b : ")
c=input("initial approx")
[r,m]=size(A)
l=1

while l~=10
    for i=1:r
        z=0
        for j=1:m
            if i~=j
                z=z+A(i,j)*c(j)
            end
        end
    c(i)=(b(i)-z)/A(i,i)
end
l=l+1
end
disp(c)

False position method or Regular falsi method

False position method or Regular falsi method



Code is Here

//false position method or regular falsi method
clear;clc;close
deff('y=f(x)','y=x^2.2-69');
printf("The given function is y=x^2.2-69 \n\n");
a=input("Enter first approximation : ");
b=input("Enter second approximation : ");
d=input("Enter accuracy : ");
printf('succesive iterations    \ta\t    b\t    f(a)\t    f(b)\t\  x1\n');
for i=1:25
    x1=b*f(a)/(f(a)-f(b))+a*f(b)/(f(b)-f(a));
    if(f(a)*f(x1))>0
        b=x1;
    else
        a=x1;
    end
    if abs(f(x1))<d
        break
    end
    printf('                         \t%f  %f  %f  %f  %f\n',a,b,f(a),f(b),x1);
end
printf('the root of the equation is  %f',x1);

Add False position method or Regular falsi method

Simpson's three by eight rule

Simpson's three by eight rule

Code is Here

clear;clc
fxn=input("Enter the fuction : (eg:y=(x^2+5*x+6)) : ")
deff('y=f(x)',fxn);
printf("The given function is %s\n\n",fxn);
a=input('Inter the lower limit : ')
b=input('Inter the upper limit : ')
n=input('Inter the value of n : ')
h=(b-a)/n
for i=0:n
    X(1,i+1)=a+h*i
    Y(1,i+1)=f(a+h*i)
end
printf("x=")
disp(X)
printf("y=")
disp(Y)
a1=Y(1,1)+Y(1,n+1);
a2=0
for j=3:3:n-1
    a2=a2+Y(1,j+1);
end
a3=0
for k=0:n-1
    p=modulo(k,3)
if p==0
else
    a3=a3+Y(1,k+1);
end
end
i=(3*h/8)*(a1+2*a2+3*a3);
printf("The value of Integral is : ")
disp(i)

Simpson's three by eight rule

ODE by Modified Euler's Method Scilab code

ODE by Modified Euler's Method Scilab code

Code is Here

ODE by Euler's Method Scilab code

ODE by Euler's Method Scilab code

Code is Here

clear
deff('z=f(x,y)','z=3*x+y/2');
printf("The given function is dy/dx=x+y\n");
X(1,1)=input('Enter the value of x0 : ')
Y(1,1)=input('Enter the value of y0 : ')
b=input('Enter the value of x : ')
n=input('Enter the value of n : ')
h=(b-X(1,1))/n
for i=2:n+1
    X(1,i)=X(1,i-1)+h
end
disp(X,"X=")
for j=2:n+1
    Y(1,j)=Y(1,j-1)+h*f(X(1,j-1),Y(1,j-1))
end
disp(Y,"y=")
printf("\nSo Value of y(%d) is = %f\n",n,Y(n+1))

ODE by Euler's Method Scilab code

Trapezoidal Method Scilab Code

Trapezoidal Method Scilab code

Code is Here

clear
fxn=input("Enter the fuction : (eg:y=(x^2+5*x+6)) : ")
deff('y=f(x)',fxn);
printf("The given function is %s\n\n",fxn);
a=input('Enter the lower limit : ')
b=input('Inter the upper limit : ')
n=input('Enter the value of n : ')
h=(b-a)/n
for i=0:n
    X(1,i+1)=a+h*i
    Y(1,i+1)=f(a+h*i)
end
printf ("x=")
disp (X)
printf ("y=")
disp (Y)
a1=Y(1,1)+Y(1,n+1);
a2=0
for j=2:n
    a2=a2+Y(1,j)
end
i=(h/2)*(a1+2*a2);
printf('The value of Integral is : ')
disp(i)

Trapezoidal Method Scilab Code

Simpson's one third (1/3) rule Scilab code

Simpson's one third (1/3) rule Scilab code

Code is Here

clear
fxn=input("Enter the fuction : (eg:y=(x^2+5*x+6)) : ")
deff('y=f(x)',fxn);
printf("The given function is %s\n\n",fxn);
a=input('Enter the lower limit : ')
b=input('Inter the upper limit : ')
n=input('Enter the value of n : ')
h=(b-a)/n
for i=0:n
    X(1,i+1)=a+h*i
    Y(1,i+1)=f(a+h*i)
end
printf ("x=")
disp (X)
printf ("y=")
disp (Y)
a1=Y(1,1)+Y(1,n+1);
a2=0
for j=2:2:n
    a2=a2+Y(1,j)
end
a3=0
for l=3:2:n-1
    a3=a3+Y(1,l)
end
i=(h/3)*(a1+4*a2+2*a3);
printf('The value of Integral is : ')
disp(i)

Simpson's one third (1/3) rule Scilab code