Numerical solution to a simple ode:
Integrate this ordinary differential equation (ode)
over the time span of 0 to 2. The initial condition is y(0) = 1.
to solve this equation, you need to create a function or function handle of the form: dydt = f(t,y) and then use one of the odesolvers, e.g. ode45.
y0 = 1; % initial condition y(t=t0) t0 = 0; tend=2; tspan = [t0 tend]; % span from t=0 to t=2 [t,y] = ode45(@myode,tspan,y0); % here is where you get the solution plot(t,y) xlabel('time') ylabel('y(t)')
Hopefully you recognize the solution to this equation is . Let's plot that on the same graph. We will use a dashed red line
hold on plot(t,exp(t),'r--') legend('numerical solution','analytical solution') % these are clearly the same solution.
ans = end
function dydt = myode(t,y)
differential equation to solve
dydt = y; % categories: ODEs % tags: math