forward euler-odes

d^2/dt^2+g*R^2/(R+x)^2

x(t=0)=0

dx(t=0)/dt=750 m/s

FORWARD Euler dt=0,1s

is this correct to find the x in t=10s.

Answer 1

[Torsten]

You should plot x and y against t to see whether Euler forward is maybe unstable for a time stepsize of dt = 0.1 and that this was the task of the exercise. At least the MATLAB integrator ODE45 gives a different result.

g = 9.81;
R = 6.37e6;
fun = @(t,y) [y(2);-g*R^2/(R+y(1))^2];
tspan = [0 10];
y0 = [0 750];
[T,Y] = ode45(fun,tspan,y0);
Y(end,:)

ans = 1×2

1.0e+03 * 7.0099 0.6520

plot(T,Y)