lab8ex1.m

matlab codes for solving ODEs, including euler method, RK methods etc, and some examples.

function lab8ex1
m = 1;
k = 8;
omega = sqrt(k/m);
t0 = 0; tf = 10;
y0 = 0.1; v0 = 0;
[t,Y] = ode45(@f,[t0,tf],[y0,v0],[],omega);
y = Y(:,1); v = Y(:,2);

figure(1);
plot(t,y,'b+-',t,v,'ro-');
legend('y(t)','v(t)=y''(t)');
grid on;

figure(2);
plot(y,v);
xlabel('y');
ylabel('v=y''');
grid on;

function dYdt = f(t,Y,omega)
y = Y(1); v = Y(2);
dYdt = [ v ; -omega^2*y ];