function no_result = circle_demo() %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Demonstration of numerical integration % % % % We integrate one quadrant of the unit % % circle, and multiply by 4 to find pi. % % % % No argument required, just type: % % >> circle_demo % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ntrials = 10; for i = 1:ntrials N = 10*i^2; % Number of steps dx(i) = 1.0/N; % Step size % Euler integral = euler_1d(0, 0, dx(i), N, 'circle'); euler_pi(i) = 4*integral(N+1); % RK2 (Midpoint method) integral = rk2_1d(0, 0, dx(i), N, 'circle'); rk2_pi(i) = 4*integral(N+1); end hold off plot(dx,euler_pi,'b') hold on plot(dx,rk2_pi,'r') plot(dx,ones(ntrials)*pi,'g--')