function [] = L12_Q03 ()
y = @(t) −t* cos(t − 1) + t
f = @(t,w) t *sin(t − 1) + w/t
y1 = 0;
w1 = 0;
t1 = 1;
tn = 10;
get_step_size();
run_eulers_method();
end
function [] = get_step_size()
h = input('Enter a step size h: ');
while h <=0 || abs(h - floor(h)) > 1e-8
fprintf('Invalid entry %d \n', steps);
h = input('Enter a step size h: ');
end
end
function [] = run_eulers_method(y,f,h, ,t1, tn, w1)
t = t1:h:tn;
wnext = w1 + h*f(t1,w1)
e = abs(y1 - w1);
fprintf('The average absolute error in the approximation is %0.5f \n', e);
plot_results();
end
function [] = plot_results(y,t1, h, tn, t, w)
figure(1);
clf;
plot(1:y, w, 'ob');
xlabel('Time');
ylabel('Function Value');
print('-dpng', 'newtons_method_approx.png');
end
