function oppgave_6_1_5

k=0:5;

% Exact solution:
% (a) 
y_exact = @(t) -t-1+exp(t);
% (b) 
%y_exact = @(t) t-1+exp(-t);


H = [];
E = [];
for k=0:5,
    h = 0.1*2^(-k);
    n = round(1/h);
    % Euler's method
    t = 0; y=0;
    for i=1:n,
        y = eulerstep(t,y,h);
        t = t+h;
    end
    H = [H,h];
    E = [E,abs(y-y_exact(1))];
end

% plot the error vs h
figure(1); clf;
fs = 24; %font size
loglog(H,E,'x-','LineWidth',3,'MarkerSize',10);
xlabel('h','FontSize',fs); ylabel('Error','FontSize',fs);
grid on;

function y=eulerstep(t,y,h)
%one step of Euler's Method
%Input: current time t, current value y,  stepsize h
%Output: approximate solution value at time t+h
y=y+h*ydot(t,y);

function z=ydot(t,y)
%right-hand side of differential equation
z =  t+y; % oppgave (a)
%z =  t-y; % oppgave (b)
%z = 4*t-2*y; % oppgave (c)