ex05ch1.m

these codes are for solving OED with matlab

function ex05ch1
% Contrast local and global error
% Initialize output arrays.
t = [];
le = [];
ge = [];
% Initialize for integration.
tn = 0;
yn = 0.08;
h = 0.1;
for i = 1:20
    tnp1 = tn + h;
    ynp1 = yn + h*ode(tn,yn);
    len = localsol(tn,yn,tn+h) - ynp1;
    gen = globalsol(tn+h) - ynp1;
    t = [t tnp1];
    le = [le len];
    ge = [ge gen];
    tn = tnp1;
    yn = ynp1;
end
plot(t,le,'o',t,ge,'*')
axis([0 2 -10 70])
legend('local error','global error',2)
%===============================================
function dydt = ode(t,y)
dydt = 5*(y - t^2);

function gy = globalsol(t)
% Global solution.
gy = t^2 + 0.4*t + 0.08;

function ly = localsol(tn,yn,t)
% Local solution.
ly = globalsol(t) + (yn - globalsol(tn))*exp(5*(t - tn));