Gaussian Quadratute Algorithm using MATLAB(m file)

MATLAB Program:

% Gaussian Quadratute Algorithm

 % Find the integral of y=sin(x) from 0 to pi.

 function integral = Gaussian_quadrature()

 a = input('Enter lower limit, a:  ');

 b = input('Enter upper limit, b:  ');

 n = input('Enter the order, n:  ');

 if (n < 2 | n > 8)

   fprintf('This code works only for order from 2 to 8\n');

 else

   a0 = 0.5*(b+a);

   a1 = 0.5*(b-a);

 if (n == 2)

   c(1) = 1.0;

   c(2) = c(1);

   x_table(1) = -0.577350269;

   x_table(2) = -x_table(1);

 elseif (n == 3)

   c(1) = 0.555555556;

   c(2) = 0.888888889;

   c(3) = c(1);

   x_table(1) = -0.774596669;

   x_table(2) = 0.0;

   x_table(3) = -x_table(1);

 elseif (n == 4)

   c(1) = 0.347854845;

   c(2) = 0.652145155;

   c(3) = c(2);

   c(4) = c(1);

   x_table(1) = -0.861136312;

   x_table(2) = -0.339981044;

   x_table(3) = -x_table(2);

   x_table(4) = -x_table(1);

 elseif (n == 5)

   c(1) = 0.236926885;

   c(2) = 0.478628670;

   c(3) = 0.568888889;

   c(4) = c(2);

   c(5) = c(1);

   x_table(1) = -0.906179846;

   x_table(2) = -0.538469310;

   x_table(3) = 0.0;

   x_table(4) = -x_table(2);

   x_table(5) = -x_table(1);

 elseif (n == 6)

   c(1) = 0.171324492;

   c(2) = 0.360761573;

   c(3) = 0.467913935;

   c(4) = c(3);

   c(5) = c(2);

   c(6) = c(1);

   x_table(1) = -0.932469514;

   x_table(2) = -0.661209386;

   x_table(3) = -0.238619186;

   x_table(4) = -x_table(3);

   x_table(5) = -x_table(2);

   x_table(6) = -x_table(1);

 elseif (n == 7)

   c(1) = 0.129484966;

   c(2) = 0.279705391;

   c(3) = 0.381830050;

   c(4) = 0.417959184;

   c(5) = c(3);

   c(6) = c(2);

   c(7) = c(1);

   x_table(1) = -0.949107912;

   x_table(2) = -0.741531186;

   x_table(3) = -0.405845151;

   x_table(4) = 0.0;

   x_table(5) = -x_table(3);

   x_table(6) = -x_table(2);

   x_table(7) = -x_table(1);

 elseif (n == 8)

   c(1) = 0.101228536;

   c(2) = 0.222381034;

   c(3) = 0.313706645;

   c(4) = 0.362683783;

   c(5) = c(4);

   c(6) = c(3);

   c(7) = c(2);

   c(8) = c(1);

 x_table(1) = -0.960289856;

 x_table(2) = -0.796666477;

 x_table(3) = -0.525532409;

 x_table(4) = -0.183434642;

 x_table(5) = -x_table(4);

 x_table(6) = -x_table(3);

 x_table(7) = -x_table(2);

 x_table(8) = -x_table(1);

end

 integral = 0.0;

 for i = 1:1:n

 x(i) = a0 + a1*x_table(i);

 f(i) = funkeval(x(i));

 integral = integral + c(i)*f(i);

 end

 integral = integral*a1;

 fprintf('The integral is: %10.8f\n\n',integral);

end

 function f = funkeval(x)

 f= sin(x);

OUTPUT:

>> Gaussian_quadrature_c
Enter lower limit, a:  0
Enter upper limit, b:  pi
Enter the order, n:  7
The integral is: 2.00000000

ans =
    2.0000>> 

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