driver.m

Integraton routines in matlab

%
%

% error function
%f = inline('exp(-x.^2)*2/sqrt(pi)', 'x');
%a = 0; b = 2;
%integ_ex = erf(b);

% bessel function
%f = inline('cos( 8*sin(x) - x )/pi', 'x');
%a = 0; b = pi;
%integ_ex = bessel(1,8);

% 
%f = inline('4./(1+x.^2)', 'x');
%a = 0; b = 1;
%integ_ex = pi;

% 
f = inline('sin(x)', 'x');
a = 0; b = pi;
integ_ex = 2;

% 
%f = inline('atan(10*x)', 'x');
%a = -3; b = 4;
%integ_ex = 4*atan(40) + 3*atan(-30) - (1/20)*log(16/9);

% 
%f = inline('exp(-50*(x-0.5).^2) + exp(-2*x)', 'x');
%a = 0; b = 1;
%integ_ex = 1;

% 
%f = inline('sin(x).^2.*cos(x).^4', 'x');
%a = 0; b = 2*pi;
%integ_ex = b/16;


disp(' ')
disp(' Use the composite Trapezoidal rule')
tol = 1.e-4;
[integ, T, nfeval] = trapcomp(f, a, b, tol);
fprintf(1,' computed integral %12.8e \n', integ)
fprintf(1,' relative error %12.8e \n', abs(integ-integ_ex)/abs(integ_ex) )
fprintf(1,' number of function values needed %6d \n', nfeval)

disp(' hit return to continue ....'); pause

disp(' ')
disp(' Use the composite Simpson rule')
tol = 1.e-4;
[int, S, nfeval] = simpcomp(f, a, b, tol);
fprintf(1,' computed integral %12.8e \n', integ)
fprintf(1,' relative error %12.8e \n', abs(integ-integ_ex)/abs(integ_ex) )
fprintf(1,' number of function values needed %6d \n', nfeval)

disp(' hit return to continue ....'); pause

disp(' ')
disp(' Use Romberg integration')
tol = 1.e-4;
[integ, R, nfeval] = romberg(f, a, b, tol);
fprintf(1,' computed integral %12.8e \n', integ)
fprintf(1,' relative error %12.8e \n', abs(integ-integ_ex)/abs(integ_ex) )
fprintf(1,' number of function values needed %6d \n', nfeval)

disp(' hit return to continue ....'); pause

disp(' ')
disp(' Use adaptive Simpson integration')
tol = 1.e-4;
hmin = 1.e-8;
[integ, xfv, nfeval] = simpadpt(f, a, b, tol, hmin);
fprintf(1,' computed integral %12.8e \n', integ)
fprintf(1,' relative error %12.8e \n', abs(integ-integ_ex)/abs(integ_ex) )
fprintf(1,' number of function values needed %6d \n', nfeval)

fv = feval(f, xfv);
plot(xfv, fv, 'o')