README.md

06_initial_value_ode

Problem 2

Script:

%Part a.
y_analytical = @(t) exp(-t);

%Part b.
dt = 0.01; %step size
a = figure(1);
set(0, 'defaultAxesFontsize', 16)
set(0, 'defaultTextFontsize', 16)
set(0, 'defaultLineLineWidth', 2)
hold on
t = [0:dt:3]';
y_n = zeros(size(t));
y_n(1) = 1; %initial condition
for i = 2:length(t)
	dy = ode2(t, y_n(i-1));
    y_n(i) = y_n(i-1) + dt*dy;
end
plot(t, y_analytical(t), 'k-', t, y_n, 'o-');
title('Analytical vs. Euler')
legend('Analytical', 'Euler', 'Location', 'Northeast')
saveas(a, 'euler.png');

%Part c.
b = figure(2);
y_heun = heun_sol_order1(@(t,y) ode2(t,y), dt, 1, [0 3]);
plot(t, y_analytical(t), 'k-', t, y_heun, 'o-');
title('Analytical vs. Heun')
legend('Analytical', 'Heun', 'Location', 'Northeast')
saveas(b, 'heun.png');

Part a.